Warm-Up Exercise 3

Due 1:00 pm, Thu, Sep. 08

Physics 313R, Fall Semester, 2011

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Did you complete the reading assignment?
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There are two string of 0's and 1's shown below. Which is "random"? That is, which looks like more what you expect from a sequence of coin tosses (imagine the faces of the coins are marked with 0 and 1 instead of heads and tails)?

001000011111111000101111100010100101110000101101011110100101110000111011100 10010010001110000011001111111110101001011011000111011011010101110010101011111 11110100000110010111000001100011000100110100010111001000111101101011101001100 10000000000010100111000000001000111011011101110110001111110101111101010001000 10101100001111001111001110001011001100011011000000001001000010011100101001011

001101010100100011001101001101100101010111001111010010001010111000001011001 00010010100110110010010101010101001010011001010101001010110010101110111010111 11010101100100001001110001000101010101001010110111001101001010010100101110110 10101010101000010010010010010111001110101011010010101010111111010100111110100 10101001000010011011010000010100101011000110100010110001111001100110110101001

Explain your answer to the last question. Defend your choice.

What is the smallest value of M for which the difference between ln(M!) and Sterling's approximation for ln(M!) differ by less than 1%?

When particles move around by diffusion, you almost get something for nothing---the particles can spread out, move around, without any work being required. Thinking microscopically, is this a good way to transport things, say, inside a bacterium? Explain your reasoning.

Explain anything that you didn't understand in the reading assignment:

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