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We have presented the kinetic study of the very initial growth stages of an ultra thin film (40 $\AA$ - 150$\AA$) of Ag sputter-deposited on Si(001) substrate containing native oxide using grazing incidence x-ray reflectivity (GIXR) technique and Atomic Force Microscopy (AFM). We observe that the film consists of mounds with the presence of voids. The thickness `$d_{xray}$' and the packing fraction `$\eta$' of the film as a function of time `$t$' follow a simple power law, $d_{xray}$ $\thicksim$ $t^{m}$ and $\eta$ $\thicksim$ $t^{n}$ with the exponent $m$ = 0.58 and $n$ = 0.37 respectively. We have quantitatively determined that the voids between the mounds decrease at the initial growth stages with the increase in mound size using GIXR measurement. The mound size increases by two distinct mechanisms. Firstly, the mound grows itself by the addition of Ag atoms or clusters (mechanism A) and secondly the adjoining mounds coalesce to form a bigger mound (mechanism B). We have observed that as a function of time the mound size $R(t)$ increases radially as $\thicksim$ $t^{z}$. The radial growth exponent $z$ crosses over from a linear regime $z$ $\thicksim$ 1 to $z$ $\thicksim$ 1/4 for mechanism A and from $z$ $\thicksim$ 0.7 to $z$ $\thicksim$ 1/4 for mechanism B at the same instant of time indicating a cross over of the radial growth exponent leading to two growth regimes. The GIXR measurement reveals sublinear dependence of $\eta$ on $d$ and the AFM measurement shows a cross over of the radial grwoth exponent, both these indicates that the lateral growth of the mound is enhanced initially reducing the voids.

The sputtering yield, Y, from a cylindrical thermal spike is calculated using a two dimensional fluid dynamics model which includes the transport of energy, momentum and mass. The results show that the high pressure built-up within the spike causes the hot core to perform a rapid expansion both laterally and upwards. This expansion appears to play a significant role in the sputtering process. It is responsible for the ejection of mass from the surface and causes fast cooling of the cascade. The competition between these effects accounts for the nearly linear dependence of $Y$ with the deposited energy per unit depth that was observed in recent Molecular Dynamics simulations. Based on this we describe the conditions for attaining a linear yield at high excitation densities and give a simple model for this yield.

The critical behavior at the frozen/active transition in the Domany-Kinzel stochastic cellular automaton (DKCA) is studied {\it via} a surface growth process in (1+1) dimensions. At criticality, this process presents a kinetic roughening transition; we measure the critical exponents in simulations. Two update schemes are considered: in the symmetric scheme, the growth surfaces belong to the Directed Percolation (DP) universality class, except at one terminal point. At this point, the phase transition is discontinuous and the surfaces belong to the Compact Directed Percolation universality class. The relabeling of space-time points in the nonsymmetric scheme alters the surface growth dramatically. The critical behavior of rough surfaces at the nonchaotic/chaotic transition is also studied using the damage spreading technique; the exponents confirm DP values for the symmetric scheme.