It was on one of these sunny days that I had a guest. He was a generous young man. Soon after he came nearby, he served his blood to the mosquitos. Considering all the things humans pick from nature, their blood is the fruit that nature can pick in return, right? Anyway, the reason that I called this guest generous is that he did not kill the mosquitos while they were sucking his blood. He sat near me, and started pondering over the nice valley below. I didn’t know at first if I should talk to him. The snail creeping on me preferred to keep silent too. So I decided not to speak to him.

Soon after, a friend of this young man arrived. They started talking about finding water here. I thought “How do you think water can be found at this height of the hill?” But they started digging with the special equipments they had. I had heard about these things when a group of students had come on a field trip. They talked about the different kinds of rocks and the minerals in them, their story of formation through the depths of the earth or under deep water, and how one could find invaluable fluids by digging through them. Seeing these two young men, I better understood what they meant.

Anyway, after a few hours of extreme noise, I felt the wetness that touched me from below. The water was indeed rising in the well the two young men had made, and soon they were screaming from joy. As they indulged in their celebration, I was engulfed by that uncomfortable feeling I had when they’d arrived. After all, this was my place, and they had invaded it.

As if this invasion wasn’t enough, the man who had arrived first stepped on me and spread a cloth. I was enraged at the thought of this man celebrating his victory over me. But my rage stumbled upon what I saw as I watched him. He started offering thanks and praying. It was then that a sense of warmth seeped between us, and I began talking to him everytime he came. During his visits, he used to drink some fresh water, sit on me looking towards the valley, and delve into reflections and prayers. I thanked God for giving me this flat surface so that someone could pray on me. Our relationship became so special that when he was not around, I used to pray for his return.

Years passed by. Things didn’t change much with me, but the man changed a lot. His once smooth face now looked like the wavy ocean surface. His body was bent like trees on steep hills. Things were changing incredibly fast for humans. I felt pity for this man who was troubled by his daily affairs. I prayed that I could be closer to him to help relieve his pains. My prayers were accepted and this respectable man spent more and more time on me. Sometimes lying, sometimes sitting, but always contemplating or praying.

At times, he brought his grandchildren. These kids did not enjoy being here as much as their grandfather. They constantly kept looking at the glasses in their hands that entertained them. But sometimes, they had funny talks with their grandfather. For example, this one time they talked about putting the stones in water or burrying them in the soil so that they can grow like plants. When I heard those words, I thought about my genesis through the ocean beds and the inferno compartments in the earth. My life story was so naively and elegantly put into those few words of the children. It is curious how the little ones can formulize complex things so easily.

Those times of amusement used to make me think about myself. I was a mature rock, and I wanted to have youngsters around me. I prayed to have little ones that were eager to “rock ‘n’ roll.” But perhaps those little ones would not show up as soon as they did for the humans, and they would not be as rambunctious as their human peers. Anyway, with my innate desire, I kept praying to have them around.

Strange enough, my prayers were answered sooner than I thought, and I started seeing these little pebbles parting from me. In my maturity, I had the blessing of giving birth to children all around me. Now, whenever the old man came with his grandchildren, they played with mine, and that gave me immense pleasure.

At last one day, I saw a group of people coming near by with a wooden box on their shoulders. Yes, that was him, brought to meet his Lord… He was burried in the cemetery at the peak of the hill.

…

You know, it’s not easy to lose someone you love. It’s feels like burying a part of your heart before you actually die. I cried a lot, and I still do, silently, in my own way. I don’t want my sorrow to assume the form of a complaint against the decree of our Lord. Yet, I cry nonetheless. Maybe this grief is what has made me so weak nowadays. I am feeling that my end is near, too. The increasing number of little ones all around is making this message impossible to ignore. But at the same time, I am developing a hope of continuity; because the water that is springing under me penetrates into my pores, and water means life.

However, the peace that comes with this hope is always followed by the grief of losing my friend, and I am crying all my water out. To quench my sorrow, God sent me lots of people. They are all around, now that my tears are making a waterfall. But I’d rather have my friend pray on me than these people laugh with negligence at my sorrow. “Oh my Lord, my friend in the heavens… Oh my Lord, my friend in the heavens…”

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).

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

1. T. Karabacak, H. Guclu, and M. Yuksel, “Network Behavior in Thin Film Growth Dynamics,” Physical Review B, 79(19), May 2009.
2. D. Winkler, “Patterns of forest distribution and the impact of fire and pastoralism in the forest region of Tibet,” In: G. Miehe and Y. L. Zhang, Editors, Environmental Changes in High Asia. Selbstverlag der Marburger Geographischen Gesellschaft, Marburg 135, pp. 201–227, 2000.
3. T. Karabacak, G.-C. Wang, and T.-M. Lu, “Physical self-assembly and the nucleation of 3D nanostructures by oblique angle deposition,” J. Vac. Sci. Technol. A 22, pp. 1778, 2004.
4. J.-X. Fu, A. Collins, and Y.-P. Zhao, “The optical properties and biosensor application of ultra thin Silver films prepared by oblique angle deposition,” J. Phys. Chem. C 112, pp. 16784–1679, 2008.
5. D.-X. Ye, Z.-P. Yang, A.S.P. Cang, J.Bur, S.Y. Lin, T.-M. Lu, R.Z. Wang, S. John, “Experimental realization of a well-controlled 3D silicon spiral photonic crystal,” J. Phys. D: Appl. Phys., 40, pp. 1, 2007.
6. P.-I. Wang, S. H. Lee, T. C. Parker, M. D. Frey, T. Karabacak, J.-Q. Lu, and T.-M. Lu, “Low temperature wafer bonding by copper nanorod array,”, Electrochem. and Solid State Lett., 12, pp. H138-H141, 2009.
7. R. Kumar, J. Novak, and A. Tomkins, “Structure and evolution of online social networks,” Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 611-617, Philadelphia, PA, August 2006.