Maxwell's Demon, Rectifiers, and the Second Law: Computer Simulation of Smoluchowski's Trapdoor

We have simulated numerically an automated Maxwell's demon inspired by Smoluchowski's ideas of 1912. Two gas chambers of equal area are connected via an opening that is covered by a trapdoor. The trapdoor can open to the left but not to the right, and is intended to rectify naturally occurring variations in density between the two chambers. Our results confirm that though the trapdoor behaves as a rectifier when large density differences are imposed by external means, it can not extract useful work from the thermal motion of the molecules when left on its own.

Qualitative and Quantitative Knowledge in Classical Mechanics

This thesis investigates what knowledge is necessary to solve mechanics problems. A program NEWTON is described which understands and solves problems in mechanics mini-world of objects moving on surfaces. Facts and equations such as those given in mechanics text need to be represented. However, this is far from sufficient to solve problems. Human problem solvers rely on "common sense" and "qualitative" knowledge which the physics text tacitly assumes to be present. A mechanics problem solver must embody such knowledge. Quantitative knowledge given by equations and more qualitative common sense knowledge are the major research points exposited in this thesis. The major issue in solving problems is planning. Planning involves tentatively outlining a possible path to the solution without actually solving the problem. Such a plan needs to be constructed and debugged in the process of solving the problem. Envisionment, or qualitative simulation of the event, plays a central role in this planning process.

On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice.