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Diffusion- L imited A ggregation

Diffusion- L imited A ggregation. A DLA cluster grown from a copper sulfate solution in an electrodeposition cell. What is DLA?. Diffusion- L imited A ggregation (DLA) is the process whereby particles undergoing a

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Diffusion- L imited A ggregation

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  1. Diffusion-Limited Aggregation A DLA cluster grown from a copper sulfate solution in an electrodeposition cell

  2. What is DLA? Diffusion-Limited Aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by Witten and Sander in 1981, is applicable to aggregation in any system where diffusion is the primary means of transport in the system. DLA can be observed in many systems such as electrodeposition, Hele-Shaw flow, mineral deposits, and dielectric breakdown. Of critical importance is that the number of particles undergoing Brownian motion in the system is kept very low so that only the diffusive nature of the system is present. T. A. Witten Jr, L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981)

  3. Our aim:

  4. Lichtenberg Figures

  5. Lichtenberg Figures

  6. Lichtenberg Figures Under continued irradiation, electrons rapidly accumulate inside the acrylic, forming a cloud-like layer of excess negative charge called a space charge. Since acrylic is an excellent electrical insulator, the electrons become trapped in the space charge layer. A huge electrical field (up to 2 million volts/cm) is developed inside the plastic, similar to the way that huge regions of excess charge develop within a thunderstorm. The tremendous electrical stress finally overcomes the insulating strength of the plastic. Molecular bonds begin to break, forming ionized (electrically conductive) pathways within the acrylic. The excess charge violently surges out, accompanied by a brilliant blue-white flash and a loud bang. The branching discharge paths look similar to a miniature lightning bolt. The high current discharge may last for only 20 – 50 billionths of a second, and smaller discharges may occur for up to 30 seconds after the main discharge.

  7. Нека да помислим какво ни е необходимо за решаване на задачата, т.е. да се опитаме да съставим т.нар. “спагети – код”: Какво искаме от програмата като краен резултат? (число, графика, т.н.) Как го искаме (в какъв вид)? (ascii файл, таблица, на екрана, т.н.) Какво е необходимо НИЕ да зададем на програмата като “вход”? (променливи, константи, масиви, начални данни/условия, т.н.)

  8. Конкретно за DLA: • Решетка (M,N) • Масив (M, N) • Генератор на случайни числа • Брой частици • Начални условия • Първа частица, място на “тръгване” • Разходка + Проверка на Гранични Условия + Проверка на Условията за DLA-”Отлагане” + запис на коoрдинатите • Нова частица... • End • The shadow effect, preliminary “treated” surface…

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