Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Constitutive Response of Passivated Copper Films: Experiments and Analyses

The constitutive behavior of passivated copper films is studied. Stresses in copper films of thickness ranging from 1000 nm to 40 nm, passivated with silicon oxide on a quartz or silicon substrate, were measured using the curvature method. The thermal cycling spans a temperature range from - 196 to 600°C. It is seen that the strong relaxation at high temperatures normally found in unpassivated films is nonexistent for passivated films. The copper film did not show any rate-dependent effect over a range of heating/cooling rate from 5 to 25°C/min. Further analyses showed that significant strain hardening exists during the course of thermal loading. In particular, the measured stress- temperature response can only be fitted with a kinematic hardening model, if a simple constitutive law within the continuum plasticity framework is to be used. The analytic procedures for extracting the film properties are presented. Implications to stress modeling of copper interconnects in actual devices are discussed.

Nonequilibrium ``Melting'' of a Charge Density Wave Insulator via an Ultrafast Laser Pulse

We employ an exact solution of the simplest model for pump-probe time-resolved photoemission spectroscopy in charge-density-wave systems to show how, in nonequilibrium, the gap in the density of states disappears while the charge density remains modulated, and then the gap reforms after the pulse has passed. This nonequilibrium scenario qualitatively describes the common short-time experimental features in TaS2 and TbTe3, indicating a quasiuniversality for nonequilibrium ``melting'' with qualitative features that can be easily understood within a simple picture.