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By de Borst R., Bicanic N., Meschke G.

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SNL SIMULATION Number of Clusters vs. 5: Average Number of Clusters vs. Number of SELs in Network (adapted from [58]). Number of Clusters vs. 6: Average Number of Clusters vs. Number of SELs in Network (adapted from [58]). 32 CHAPTER 3. 2. Radius for Packing N Circles in the Unit Square. 036583075322 Consider the SNL problem with circular broadcast range inside the circle of radius r: 1. The SEL location serves as the center of the broadcast circle, and thus all centers of the circles must be in the unit square.

2. 26) 3. 26) for the two unknowns: fx and fy and form the gradient as (fx , fy ). ¨ CHAPTER 4. COORDINATE FRAMES AND GRADIENT CALCULATION 54 Polynomial Approximation: Plane (GA3) For each device, the position must be known. To approximate the gradient: 1. 27)  =  ..     . a2 1 enx eny f (en ) 2. 27) for a0 , a1 , and a2 . 3. The gradient is then (a1 , a2 ). 28) 1 + (Sx − x)2 + (Sy − y)2 where Dmax is the maximum value of the function at the source location (Sx , Sy ). 28) as follows: √ 1 + (Sx − x)2 + (Sy − y)2 1 = f (x, y) Dmax 1 1 + (Sx − x)2 + (Sy − y)2 = 2 f 2 (x, y) Dmax u(x, y) = a0 + a1 x + a2 y + a3 x2 + a4 y 2 where u(x, y) = a4 = D21 .

In addition, there are some problems with shoehorning codes into the simulator (specified node connections may not occur in the simulator). In the actual motes, new batteries need to be used for benchmarking and testing to get consistent results. 5. SUMMARY AND CONCLUSIONS 41 clock setting influences the correctness of the leadership protocol: set to 32 ticks/sec is really good; 64 ticks/sec results in failure about half the time, and 100 ticks/sec leads to high failure rates. In addition, delay timings are crucial for Phase I of the leadership protocol.

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