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In this study we try to answer the qustion : What happens when explicitconstraints are introduced such that the low energy, long wavelength modes of asystem are unavailable ? This question has assumed some importance in recentyears due to the advent of nano technology and the growing use of nanometerscale devices and structures. In a small system, the size limits the scale ofthe fluctuations and makes it imperative for us to understand how the responseof the system is altered in such a situation. In this thesis, this question isanswered for the special case of interfacial fluctuations in two dimensions(2d). The energy of an interface between two phases in equilibrium is invariantwith respect to translations perpendicular to the plane (or line in 2d) of theinterface. We study the consequence of breaking this symmetry explicity usingan external field gradient. One expects that since low energy excitations aresuppressed, the interface would be flat and inert at all times. We show thatsurprisingly there are novel fluctuations and phenomena associated with suchconstrained interfaces which have static as well as dynamic consequences. TheIsing interface on a square lattice is shown to undergo a multitude ofstructural transitions as a function of velocity and the orientation. Liquidsolid interfaces show coherent addition and removal of atomic layers providingnovel mechanisms of stress relaxation in a nanosized single crystal withoutdefects. We study momentum and energy transfer across the liquid solidinterface in the presence of this ``layering'' transition.Comment: Based on the thesis submitted to Jadavpur University for a Ph.D.  degre

Growing Smooth Interfaces with Inhomogeneous Moving External Fields: Dynamical Transitions, Devil’s Staircases, and Self-Assembled Ripples