We propose computational sensor networks as a methodology to exploit models of physical phenomena in order to better understand the structure of the sensor network. To do so, it is necessary to relate changes in the sensed variables (e.g., temperature) to the aspect of interest in the sensor network (e.g., sensor node position, sensor bias, etc.), and to develop a computational method for its solution. As an example, we describe the use of the heat equation to solve the sensor localization problem. Simulation and physical experiments are described.

This paper presents an out-of-core approach for interactive streamline construction on large unstructured tetrahedral meshes containing millions of elements. The out-of-core algorithm uses an octree to partition and restructure the raw data into subsets stored into disk files for fast data retrieval. A memory management policy tailored to the streamline calculations is used such that, during the streamline construction, only a very small amount of data are brought into the main memory on demand. By carefully scheduling computation and data fetching, the overhead of reading data from the disk is significantly reduced and good memory performance results. This out-of-core algorithm makes possible interactive streamline visualization of large unstructured-grid data sets on a single mid-range workstation with relatively low main-memory capacity: 5-15 megabytes. We also demonstrate that this approach is much more efficient than relying on virtual memory and operating system's paging algorithms.

Streamline construction is one of the most fundamental techniques for visualizing steady flow fields. Streamribbons and streamtubes are extensions for visualizing the rotation and the expansion of the flow. The paper presents efficient algorithms for constructing streamlines, streamribbons, and streamtubes on unstructured grids. A specialized Runge-Kutta method is developed to speed up the tracing of streamlines. Explicit solutions are derived for calculating the angular rotation rates of streamribbons and the radii of streamtubes. In order to simplify mathematical formulations and reduce computational costs, all calculations are carried out in the canonical coordinate system instead of the physical coordinate system. The resulting speed up in overall performance helps explore large flow fields.

The bisection method provides an affirmative answer for scalar functions. We show that the answer is negative for bivariate functions. This means, in particular, that an arbitrary continuation method cannot approximate a zero of every smooth bivariate function with non-zero topological degree.

We find lower and upper bounds on the complexity, comp(deg), of computing the topological degree of functions defined on the n -dimensional unit cube C n , f : C n → R n , n ≥ 2, which satisfy a Lipschitz condition with constant K and whose infinity norm at each point on the boundary of C n is at least d , d > 0, and such that K 8d ≥ 1 . A lower bound, comp low ≅ 2n( K 8d ) n−1 (c + n) is obtained for comp(deg), assuming that each function evaluation costs c and elementary arithmetic operations and comparisons cost unity. We prove that the topological degree can be computed using A = (⌊ K 2d + 1⌋ + 1) n − (⌊ K 2d + 1⌋ − 1) n function evaluations. It can be done by an algorithm ϕ ∗ due to Kearfott, with cost given by comp (ϕ ∗ ) ≅ A (c + ( n 2 2 )(n − 1)!) . Thus for small n, say n ≤ 5, and small K 2d , say K 2d ≤ 9 , the degree can be computed in time at most 10 5 ( c + 300). For large n and/or large K 2d the problem is intractable.