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COS 126 – Atomic Theory of Matter

COS 126 – Atomic Theory of Matter. Announcements. Project – due Friday (1/12) midnight TA Office Hours this week (check website) Lab Help (Mon-Fri 7pm-9pm) Output should EXACTLY match examples Can use Diff.java (9.6) Start early…. Exam 2 – Pickup from your TA. Atomic Theory Overview.

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COS 126 – Atomic Theory of Matter

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  1. COS 126 – Atomic Theory of Matter

  2. Announcements • Project – due Friday (1/12) midnight • TA Office Hours this week (check website) • Lab Help (Mon-Fri 7pm-9pm) • Output should EXACTLY match examples • Can use Diff.java (9.6) • Start early…. • Exam 2 – Pickup from your TA

  3. Atomic Theory Overview • Brownian Motion • Random collision of molecules • Displacement over time fits a Gaussian distribution

  4. Atomic Theory Overview • Avogadro’s Number • Number of atoms needed to equal substances atomic mass in grams • NA atoms of Carbon-12 = 12 grams • Can calculate from Brownian Motion • Variance of Gaussian distribution is a function of resistance in water, number of molecules

  5. Bead.java • Represent particles (beads) in water • API • public Bead() • public void add(int i, int j) • public int mass() // number of pixels • public double distanceTo(Bead b) // from center (average) • public String toString() • Only need 3 values to efficiently store • Thoroughly test (simple main)

  6. BeadFinder.java • Locate all beads in a given image • API • public BeadFinder(Picture picture, double threshold) • Calculate luminance (see Luminance.java, 3.1) • Count pixels with at luminance > threshold • Find beads with DFS (see Percolation.java, 2.4) • The hard part, next slide… • public Bead[] getBeads(int minSize) • Returns all beads with at least minSize pixels • Array must be of size equal to number of beads

  7. Bead Finder - Depth First Search • Use boolean[][] array to mark visited • Traverse image • Dark pixel – mark as visited, continue • Light pixel – create new bead, call dfs • DFS algorithm • If pixel out-of-bounds, return • If pixel has been visited, return • If pixel is dark, mark + return • Add pixel to current bead, mark as visited • Recursively visit up, down, left, right

  8. Bead Finder - Depth First Search • Use boolean[][] array to mark visited • Traverse image • Dark pixel – mark as visited, continue • Light pixel – create new bead, call dfs • DFS algorithm • If pixel out-of-bounds, return • If pixel has been visited, return • If pixel is dark, mark + return • Add pixel to current bead, mark as visited • Recursively visit up, down, left, right

  9. Bead Finder - Depth First Search • Use boolean[][] array to mark visited • Traverse image • Dark pixel – mark as visited, continue • Light pixel – create new bead, call dfs • DFS algorithm • If pixel out-of-bounds, return • If pixel has been visited, return • If pixel is dark, mark + return • Add pixel to current bead, mark as visited • Recursively visit up, down, left, right

  10. Bead Finder - Depth First Search • Use boolean[][] array to mark visited • Traverse image • Dark pixel – mark as visited, continue • Light pixel – create new bead, call dfs • DFS algorithm • If pixel out-of-bounds, return • If pixel has been visited, return • If pixel is dark, mark + return • Add pixel to current bead, mark as visited • Recursively visit up, down, left, right

  11. Bead Finder - Depth First Search • Use boolean[][] array to mark visited • Traverse image • Dark pixel – mark as visited, continue • Light pixel – create new bead, call dfs • DFS algorithm • If pixel out-of-bounds, return • If pixel has been visited, return • If pixel is dark, mark + return • Add pixel to current bead, mark as visited • Recursively visit up, down, left, right

  12. Bead Finder - Depth First Search • Use boolean[][] array to mark visited • Traverse image • Dark pixel – mark as visited, continue • Light pixel – create new bead, call dfs • DFS algorithm • If pixel out-of-bounds, return • If pixel has been visited, return • If pixel is dark, mark + return • Add pixel to current bead, mark as visited • Recursively visit up, down, left, right

  13. BeadTracker.java • Track beads between successive images • Single main function • Take in a series of images • Output distance traversed by all beads for each time-step • For each bead found at time t+1, find closest bead at time t and calculate distance • Not the other way around! • Don’t include if distance > 25 pixels (new bead)

  14. Avogadro.java • Analyze Brownian motion of all calculated displacements • Lots of crazy formulas, all given, pretty straightforward • Be careful about units in the math, convert pixels to meters, etc.

  15. Random Thoughts… • BeadTracker and Avogadro are separate clients, must recompile both • Can still do Avogadro without other parts working, use sample input • Only keep at most two pictures open at a time (run out of memory otherwise) • Output format - System.out.printf() • "%6.3f" -> _2.354 • "%10.4e" -> 1.2535e-23

  16. Announcements • Project – due Friday (1/12) midnight • TA Office Hours this week (check website) • Lab Help (Mon-Fri 7pm-9pm) • Output should EXACTLY match examples • Can use Diff.java (9.6) • Start early…. • Exam 2 – Pickup from your TA

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