Understanding the dynamics involved in the formation and development of physical structures on both atomic and galactic scales has been a key topic for the scientific investigation since the beginning of scientific inquiry. These dynamics can be driven by many different factors such as gravity, molecular relationships, and atomic/electron interactions. The characteristics of the dynamics are critical as they are responsible for the final shape of the physical structures. Scientists have been explaining the final formations of physical structures by means of the main factor(s) of the dynamics. For example, molecular structures are explained via chemical bonds, wind patterns via pressure gradient, ocean streams via temperature gradient, and tree shapes and galaxies via gravity. In this essay, we take a brief look at the two dynamic effects believed to drive the final shapes of various physical structures from nano to macro scales: shadowing effect and reemission effect.

Shadowing effect: the game of who is taller
When sunlight falls on Earth, some shadowy areas do not receive it due to an elevated structure nearby. This causes the shadowy areas to have a different set of plants, which are usually shorter and smaller than the plants in the sunny areas. In brief, the shadowing effect is the input (here sunlight) reception behavior caused by height differences across a surface. The game here is that the taller ones grab more input than the shorter ones. In systems where the input is some kind of material falling on the surface, the most important outcome of the shadowing effect is slowly-rising columnar structures. The ultimate surface morphology depends heavily on the strength of the shadowing effect. Hills of snow following a heavy snow fall and forests with trees of various heights are examples of the shadowing effect.

Reemission effect: the game of reflections
When things bounce, they follow certain physical rules. When you throw something, it may stick or bounce depending on several factors. For instance, when the light falls onto a surface, some of it penetrates the surface and gets absorbed while the rest gets reflected. Reemission is another name for bouncing or reflection in physics, though the idea is not just equivalent angle reflection or equivalent reaction force bouncing.

Figure 1 illustrates the shadowing and reemission effects on a sample surface with hills. Falling particles will most often hit the hills first due to the shadowing effect. If the hill cannot grab the particle on the first hit, then the particle reemits, and it becomes possible for the particle to fall into a valley. In order for a particle to settle in a valley (e.g., particle B in Figure 1), it will have to go through a sequence of reemissions. Let’s say that a particle’s reemission probability (i.e., residual of the sticking coefficient) is p during a hit onto the surface. By simple math, if k reemissions are needed in order for a particle to settle in a valley point, then the probability of this valley point grabbing a particle is while it is for a hilltop under no shadow. In this very approximate model, k will be larger for a deeper valley point, thereby further reducing the grab probability. To get a quick sense of it, for p=0.5, the grab probability is 50% for a hilltop and 25%, 12.5%, and 6.25% for valley points with k=1, 2, and 3 respectively. Similarly, the parameter p represents the importance the of reemission effect in the growth of the surface. Higher p means more reemissions and a larger grab probability for valley points. That is, for p=0.9 (which means the material reemits 90% of the time), the grab probability is 10% for a hilltop; and 9%, 8.1%, and 7.3% for k=1, 2, and 3 respectively.

Intuitively, when the shadowing effect is dominant, the hills will grow larger and maybe merge with each other while sites at the valleys will remain short. The final surface will not be smooth but rough. Figure 2 shows this phenomenon on the macro scale for Tibetan forest growth under the shadowing effect, and Figure 3 shows it on the nano scale (1 nanometer corresponds to 1 billionth of a meter or about hundred thousand times smaller than the diameter of a human hair) for growth of nanostructures like nanorods (i.e., sticks at nanometer lengths). When the reemission effect is dominant, one can expect that the hills will get eliminated as the valleys will quickly grab the reemitted particles. In this case, the final surface will be smooth with evenly distributed growth.

Scientists have been using these effects to control the growth of the surface, especially recently for nanostructure growth. By changing the material characteristics (which affects the reemission probability) or the angle at which the atoms arrive at the surface (which affects shadowing), the scientist can control the dominance of the shadowing or reemission effects [3]. The final outcome of the nanostructures depends on other factors as well, such as (i) temperature of the substrate surface, (ii) energy of the particles, (iii) movement of the underlying substrate, and (iv) the initial pattern of the substrate as in Figure 3(b). By using a combination of these techniques, designers have been able to grow interesting structures such as nanosprings as shown in Fig. 3(b), or nanoballs as in Fig. 3(c). These nanostructures attracted the interest of researchers for various applications such as biosensors [4], engineering of light propagation [5], and microchip production [6].

A social perspective
It is not hard to see the role of shadowing and reemission effects on people and social growth as well. One typical tendency is that well-connected and well-known people or institutions are more likely to grab attention of newcomers to a society or a network. This phenomenon has been regularly observed in the growth of online social networks (e.g., Facebook) [3]. Similarly, wealthier people are more likely to receive a larger share of the aggregate social revenue, which yields a highly skewed wealth distribution. These social trends exist for valuable goods (i.e., “attention” in the former example and “money” in the latter) which have a high “sticking coefficient” and less reemission probability. A well-known phrase to describe this is “the rich get richer,” which Figure 3(a) clearly reveals, showing nanorod growth with a highly sticky material, silicon.

“Equal sharing” in societies is certainly achievable through a more dominant reemission effect. An analogy between reemissions and charity (or helping others) is plausible. Again, the social tendency has been to equally share (or reemit) items that are mostly commodity. Water, electricity, education, and health are examples of such commodities that people “reemit” in many societies, though even the water is not reemitted in some societies.

Conclusions
The interesting observation we would like the reader to recognize here is that shadowing and reemission effects take place at nano as well as at macro levels, and both play important roles in shaping formations or structures. Though these effects are mainly studied in physical structures, they certainly exist in unphysical structures such as societies. Sharing both physical wealth and knowledge is strongly advised for a strong community that lives in harmony. This is similar to the reemission effect during the growth of materials on the nano scale, in which reemission leads to smoother and denser films with structural integrity. On the other hand, when reemission is poor and the shadowing effect is dominant, it leads to isolated structures that look nicer but are structurally fragile (See Figure 3).

Murat Yuksel, Tansel Karabacak, and Hasan Guclu

Dr. M. Yuksel is an Assistant Professor at the Computer Science and Engineering Department of the University of Nevada, Reno. Dr. T. Karabacak is an Assistant Professor at the Applied Science Department of the University of Arkansas at Litte Rock. Dr. H. Guclu is an Assistant Professor at the Biostatistics Department of the University of Pittsburgh.

References
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of 3D nanostructures by oblique angle deposition,” J. Vac. Sci. Technol. A 22, pp. 1778, 2004.
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