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The problem of finding minimum (local as well as absolute) path lengths joining given points (or terminals) on a plane is known as the Steiner problem. The Steiner problem arises in finding the minimum total road length joining several towns and cities. We study the Steiner tree problem using six-pin soap films. Experimentally, we observe spanning trees as well as Steiner trees partly by varying the pin diameter. We propose a possibly exact expression for the length of a spanning tree or a Steiner tree, which fails mysteriously in certain cases. [ABSTRACT FROM AUTHOR]

We describe a simple experiment on the diffraction of monochromatic light by interfering liquid surface waves. The surface wave profile, which acts as a reflection phase grating for incident light, is generated by electrically driven vertical oscillations of two or more slightly immersed exciters. The theoretical intensity of the diffracted light agrees well with observations. In particular, we show the relation between the intensity and the amplitude (height) of the surface wave. Although invisible to the naked eye, the interference of liquid surface waves can be optically detected from the characteristic features of the diffraction pattern. In addition, we can measure the amplitude, wavelength, and phase velocity of the surface wave that propagates along the line joining the exciters. [ABSTRACT FROM AUTHOR]

Modern materials science requires efficient processing and characterization techniques for low dimensional systems. Raman and photoluminescence spectroscopy are important nondestructive tools which provide much information about such systems. Commercial Raman spectrometers are expensive. We discuss a less expensive apparatus with assembled collection optics. Studies of Ge nanoparticles, porous silicon (nanowire), carbon nanotubes, and two-dimensional InGaAs quantum layers demonstrate that this apparatus is useful for teaching and research on nanomaterials. [ABSTRACT FROM AUTHOR]