• Spatial Distribution of VEGF Isoforms and Chemotactic Signals in the Vicinity of a Tumor (pdf)

    Alexander R. Small, Adrian Neagu, Franck Amyot, Dan Sackett, Victor Chernomordik, Amir Gandjbakhche

    Journal of Theoretical Biology, 252, 593-607 (2008)

    This manuscript describes a reaction-diffusion model of Vascular Endothelial Growth factor (a molecule responsible for the growth of blood vessels) being released from a tumor and interacting with the tissue. We explain a number of significant experimental results with our model, and rule out a common hypothesis. This model was first developed on the back of a napkin over a lunch break during the angiogenesis workshop at the UCLA Institute for Pure and Applied Mathematics (May 2006). It was a fun workshop and a fun project, and we're exploring extensions and applications of the model right now.

  • Enhancing Diffraction-Limited Images Using Properties of the Point Spread Function (pdf)
    Alexander R. Small, Ilko Ilev, Victor Chernomordik, and Amir Gandjbakhche
    Optics Express, 14, 3193 (2006)

    This paper won me an NIH Fellow's Award for Research Excellence. It describes a really simple way to get information on fluorescent probes separated by less than the diffraction limit. I'm working right now on applying this algorithm to speeding up a super-resolution method that others have developed. Aside from the fact that it can do some neat tricks (alone or in combo with other methods), the key insight is that it shows which parts of the diffraction-limited image carry the most information.

  • Delocalization of Classical Waves in Highly Anisotropic Random Media (pdf)
    Alexander R. Small and David Pine
    Physical Review E, 75, 016617 (2007)
    *Selected for inclusion in the Virtual Journal of Biological Physics, February 1, 2007

    This paper describes a third of my thesis work. Of the three projects that went into my thesis, this one was most uniquely mine, conceived entirely on my own without any suggestions.  Of the papers that I've been an author on thus far, this is the one that I'm proudest of. It may not have turned the world upside down, but it proved to me that I am an independent scientist. This one is my baby. It describes interesting phenomena related to Anderson localization of light in layered systems. More specifically, it describes ways that Anderson localization can be thwarted, resulting in diffusive transport in systems that exhibit 1D characteristics.

    I don't know how it got selected for the Virtual Journal of Biological Physics, because it has nothing to do with biology. I guess it must have been because it's a Physical Review E article with an author at NIH. The study of waves in layered systems is indeed important for tissue optics, but Anderson localization is not known to occur in tissue optics. Well, if it ever is observed, maybe everybody will cite my paper. So that's something.


  • Scattering Properties of Core-Shell Particles in Plastic Matrices (pdf)
    Alexander R. Small, Sheng Hong, and David Pine
    Journal of Polymer Science, Part B-Polymer Physics, 43, 3534 (2005)

    This paper describes a project done in collaboration with industrial scientists at Arkema. We were working on finding ways to reduce the amount of scattering from small rubber particles embedded in plastic. The rubber particles make the plastic tougher, but they scatter light. We came up with some design rules. It was a fun project because I learned that I could do things with theoretical physics that people might actually find useful.
  • Patterned Polymer Photonic Crystals Using Holographic Lithography and Soft Lithography (pdf)
    Jun Hyuk Moon, Alexander R. Small, Gi-Ra Yi, Seung-Kon Lee, Won-Seok Chang, David J. Pine, Seung-Man Yang
    Synthetic Metals, 148, 99 (2005)

    This paper describes the part of grad school where I learned how to make lemonade from lemons. I was getting nowhere with my efforts to make good colloidal crystals in the channels of a PDMS stamp (soft lithography). Then I noticed that another student in the lab (Jun Hyuk Moon) was making polymer photonic crystals by holographic lithography. And I thought to myself "Hey, why not pattern the polymer with the stamps as well as the light? Then we could get wave guide geometries!" So I talked to Jun Hyuk and we decided to try it. And it worked.