Imagine a (16 X 16 inch) square, with two concentric squares (8 X 8 inch) and (4 X 4 inch) within it with different temperature zones in each and different coefficient of expansion (sigma1, sigma2 and sigma3) for each. The temperature is directly proportional to the perimeter of the squares. The outermost square is the hottest, and temperature decreases towards the centre. Let us name the outermost square as ABCD. 4 bugs start from its 4 corners and starts moving towards the bug in front of it at the shortest distance apart with an initial speed 1 inch per minute. The speeds of the bugs are directly proportional to the temperature zones. When will they meet? At what distance from A will they meet each other?