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Ioannis K. Dassios1

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MACSI, Department of Mathematics & Statistics, University of Limerick, Irelandioannis.dassios@ul.ie

An economic model for the national income of a union

of countries with interactions

We will assume a union of countries where each national economy interactswith the other.

Firstly, we will propose a new model where delayed variables are incorpo-rated into the system of equations and the interaction element is restrictedinto the annual governmental expenditure that is determined according tothe experience of the total system and in exports-imports of the countriesthat form the union.

Furthermore we will study stability properties, robustness and appropriatecontrol actions as well as the total system design in order to obtain a stable

situation.

Finally, we will study a practical application that will provide further in-sight and better understanding as regards the control actions, system designand produced business cycles, by considering real data of a union of countries.

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Steel microstructure to lattice mapping and plasticity

formulation to lattice

We will propose a site-bond model to simulate the elastic and plastic prop-erties of isotropic materials.

Focus will be given (a) in the mathematical derivation of the behavior oflattice elements, vertices and edges, in the presence of plastic deformations,(b) in the translation of the mathematical description with selected optioninto the matrix formulation necessary for software implementation and (c) onevaluation of options for numerical implementation, such as the introduction

of plasticity either by non-linear edge behavior (stiffness-based approach) orby non-local potential (force-based approach), to determine the most suitablefor creating the desired code.

The output of this project will be a documented code with allowance forelasticity, plasticity and damage in lattices. This is the key tool for explicitanalysis of micro-crack populations in plastically deforming steels.

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