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The free boundary condition and the inverse finite element method are the two new theoretical and numerical tools respectively, that have been developed and implemented in this dissertation to study a wide variety of complex transport processes. The inverse finite element method, an improvement of an existing isotherm method, has been developed in order to calculate the shape and position of material lines of characteristic properties such as change of phase and solidification fronts. The free boundary condition has been developed in connection with processes on truncated domains by synthetic outflow boundaries. The inverse finite element method has been implemented to the process of metal casting. A complete two-dimensional description of this process yields empirical correlations between the length and the shape of the solidification front and the process parameters or dimensionless numbers which may simplify process control of metal casting. Well known results of previous approximate modeling of this process are evaluated. It is further shown how the inverse finite element method can be implemented to a similar process of continuous production of composite materials. In the liquid phase, these materials are fiber suspensions that exhibit non-Newtonian rheological behavior modeled by integral constitutive equations. To characterize these materials rheologically, an analytic solution to the rheological equation of state for fiber suspensions is produced which is a prerequisite of modeling processing of these materials. The free boundary condition has been implemented to confined and free surface flows. In confined flows, solutions on truncated domains have been achieved, saving considerable computational time, since in other existing approaches accurate predictions were obtained only with much longer domains. A theoretical interpretation of the free boundary condition, which leads to computational results in agreement with benchmark solutions, is presented. In steady and transient free surface flows, the a priori unknown physics of the flow at the artificial outflow boundary are captured, which allows vertical and solitary waves to proceed and exit undistorted and realistic leveling rates are predicted that compare well with available experimental data. In transition regions from confined to free surface flow, predicted locations of the free surface and axial velocity profiles agree with experimental data too.

The rules of GATT prescribe the circumstances under which it is unfair to act in a manner which is otherwise acceptable international trading behavior. The problem for the GATT system and for relations among its contracting parties is that states often do not comply with GATT rules and dispute settlement decisions. Since GATT neither monitors nor enforces GATT compliance, this study argues that when the US government unilaterally prosecutes East Asian unfair trading practices, it acts as an agent for all the contracting parties to the GATT and promotes more rule-oriented diplomacy. The study is based on the evidence of 13 cases of disputes regarding unfair trading practices by Japan, China, South Korea, Taiwan, and Singapore initiated under US antidumping, countervailing duty, and Section 301 trade laws. The evidence of the cases tends to show that the implementation of American trade policy with respect to bilateral trade dispute with East Asian states is more strongly influenced by GATT rules and procedures than by domestic political and foreign policy considerations. The study shows that American power is always present in bilateral trade dispute settlement. However, the US government generally employs its power to make East Asian trading practices more GATT compliant. The study finds that the settlements which ended the disputes typically made East Asian trading practice more GATT compliant. In US-initiated disputes regarding unfair trading practices with East Asian states, settlement is found to depend upon four process variables: the ability of the US government to communicate its commitment to resolve the dispute, the ability of the US government to find political cover for the East Asian government, the credible commitment of US power, and the East Asian government's willingness to settlement the dispute. Agreement compliance is found to depend upon the quality of the agreement draft and the adequacy of the monitoring procedures. The study includes description and analysis of the US antidumping, countervailing duty, and Section 301 processes and concludes with theoretical and policy implications of the study findings.