On free surface problems: Methods of variational and quasi variational inequalities

1975 ◽  
pp. 129-148 ◽  
Author(s):  
J. L. Lions
Keyword(s):  
Free Surface ◽  
Variational Inequalities

A free surface problem arising in the drainage of a uniformly irrigated field: Existence and uniqueness results

1984 ◽  
Vol 36 (3) ◽  
pp. 389-403 ◽  
Author(s):  
John Van Der Hoek ◽  
C. J. Barnes ◽  
J. H. Knight
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Value Problem ◽  
Variational Inequalities ◽  
Existence And Uniqueness ◽  
Free Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Tile Drains ◽  
Porous Soil

AbstractA field comprising uniformly porous soil overlying an impervious subsoil is drained through equally spaced tile drains placed on the boundary between the two layers of soil. When this field is subject to uniform irrigation, a free boundary forms in the porous region above the zone of saturation. We study the free boundary value problem which thus arises using the theory of variational inequalities. Existence and uniqueness results are established.

On the role of tin underlays for the prevention of thermal grooving in thin gold films

1986 ◽  
Vol 44 ◽  
pp. 732-733
Author(s):  
Jin Young Kim ◽  
R. E. Hummel ◽  
R. T. DeHoff
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Grain Boundary ◽  
Beneficial Effect ◽  
Failure Mechanism ◽  
Failure Mechanisms ◽  
Distinct Advantage ◽  
Gold Films ◽  
Gold Thin Film

Gold thin film metallizations in microelectronic circuits have a distinct advantage over those consisting of aluminum because they are less susceptible to electromigration. When electromigration is no longer the principal failure mechanism, other failure mechanisms caused by d.c. stressing might become important. In gold thin-film metallizations, grain boundary grooving is the principal failure mechanism.Previous studies have shown that grain boundary grooving in gold films can be prevented by an indium underlay between the substrate and gold. The beneficial effect of the In/Au composite film is mainly due to roughening of the surface of the gold films, redistribution of indium on the gold films and formation of In2O3 on the free surface and along the grain boundaries of the gold films during air annealing.

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