Two Convergence Problems for Robots on Graphs

Convergence Problems in the Eurozone

Olsztyn Economic Journal ◽

10.31648/oej.3431 ◽

2012 ◽

Vol 7 (2) ◽

pp. 315-327

Author(s):

Tomasz Wierzejski ◽

Małgorzata Siemionek

Keyword(s):

Economic Efficiency ◽

Empirical Data ◽

Current Analysis ◽

Recent Period ◽

Macroeconomic Indicators ◽

Convergence Problems

This paper analyses the issue of convergence in the Eurozone. The overarching objective was to evaluate the monetary and fiscal convergence of the countries in the Eurozone during the recent period. A further goal was to establish recommendations boosting the economic efficiency of the analysed currency integration of the Eurozone. The paper pinpoints crucial theoretical underpinnings and the current analysis of the Eurozone. Empirical data pertinent to macroeconomic indicators, which were collated and statistically analysed, were also used to delineate crucial issues of convergence in the Eurozone.

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Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth

Journal of Fluid Mechanics ◽

10.1017/s0022112002002112 ◽

2002 ◽

Vol 470 ◽

pp. 319-357 ◽

Cited By ~ 88

Author(s):

ODD M. FALTINSEN ◽

ALEXANDER N. TIMOKHA

Keyword(s):

Finite Depth ◽

Modal System ◽

Full Account ◽

Inviscid Flows ◽

State Response ◽

Linear Damping ◽

Convergence Problems ◽

Run Up ◽

Fourth Order Polynomial ◽

Good Agreement

The modal system describing nonlinear sloshing with inviscid flows in a rectangular rigid tank is revised to match both shallow fluid and secondary (internal) resonance asymptotics. The main goal is to examine nonlinear resonant waves for intermediate depth/breadth ratio 0.1 [lsim ] h/l [lsim ] 0.24 forced by surge/pitch excitation with frequency in the vicinity of the lowest natural frequency. The revised modal equations take full account of nonlinearities up to fourth-order polynomial terms in generalized coordinates and h/l and may be treated as a modal Boussinesq-type theory. The system is truncated with a high number of modes and shows good agreement with experimental data by Rognebakke (1998) for transient motions, where previous finite depth modal theories failed. However, difficulties may occur when experiments show significant energy dissipation associated with run-up at the walls and wave breaking. After reviewing published results on damping rates for lower and higher modes, the linear damping terms due to the linear laminar boundary layer near the tank's surface and viscosity in the fluid bulk are incorporated. This improves the simulation of transient motions. The steady-state response agrees well with experiments by Chester & Bones (1968) for shallow water, and Abramson et al. (1974), Olsen & Johnsen (1975) for intermediate fluid depths. When h/l [lsim ] 0.05, convergence problems associated with increasing the dimension of the modal system are reported.

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