Dr. Karl Saunders
From Physics
Dr. Karl Saunders, ksaunder@calpoly.edu (805-756-1696), updated 6/06
STUDENTS: The availability of research positions and projects will vary over time. If there is a research topic or project that you would like to work on please get in touch with me. If you just want to learn more or chat about my research interests, let me know.
PUBLICATIONS: My condensed matter publications can be accessed here (http://arxiv.org./find/cond-mat/1/au:+saunders_k/0/1/0/all/0/1) and my pattern formation publication can be accessed here (http://arxiv.org./find/grp_nlin/1/au:+saunders_k/0/1/0/all/0/1)
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Primary Research Interests
- Landau Theory for de Vries Smectic Liquid Crystals
De Vries smectic liquid crystals are a new type of liquid crystal that exhibit very unusual behavior- the smectic A phase is more disordered the closer it is (e.g. in temperature) to the more ordered smectic C phase. There are also several associated features that make these liquid crystals very fun to study. Their behavior is significant both scientifically and technologically for liquid crystal displays. I am currently developing a Landau theory that models de Vries liquid crystals. Landau theory is a powerful theoretical tool from Condensed Matter physics that can be used to study phase transitions.
Interested? Students interested in working with me on this should be mathematically proficient. Thermal physics would be useful but is not crucial.
- Pattern Formation in Nonlinear Optical Systems
Pattern formation is a relatively new and cross disciplinary field of study. It is seen in physics (e.g. Rayleigh-Benard convection), chemistry (e.g. reaction-diffusion systems) and biology (e.g animal coats). Nonlinear optical systems display a very wide range of controllable pattern formation behaviors which makes them wonderful to study. I am interested in the theoretical analysis of these systems and I have been collaborating with Drs Sharpe and Sungar who have set up such a system here at Cal Poly. Visit the lab here (http://www.calpoly.edu/~jsharpe/pattern_expts.htm). One interesting feature that we studied was the control of patterning through the periodic alternation of a parameter (laser intensity). We recently published a paper (http://link.aps.org/doi/10.1103/PhysRevLett.96.094101) on this work I am currently extending the theoretical analysis we did for this particular system to more general systems. In the near(ish) future I would like to develope a model for the fluctuations and "elasticity" of such systems- there are reasons to think that they could be quite fundamentally different from condensded matter systems. Of related interest is how nonlinear optical systems are affected by "disorder" and pinning.
Interested? Mathematical enthusiasm would be important for students working on this research.
Secondary Research Interests
- The Dynamics of Driven Disordered Extended Media - "Depinning"
Everyday examples of extended media are sheets of rubber or jello. More technical sounding examples are charge density waves (CDWs) in anisotropic conductors and vortex lattices (VLs) in type II superconductors. Disorder for sheets of rubber or jello could be a rough surface like very coarse sandpaper, while for CDWs and VLs it takes the form of ionic and magnetic impurities. When a small driving force is applied to the medium, the dirt will act to prevent it from moving or, in other words, it will pin it. As with friction, once a large enough force is applied the medium will start to move or depin. The main element of my research is the nature of this depinning. Is it sudden or gradual? Does it stop moving at the same force it started moving? Do CDWs and VLs depin more like rubber or jello?
- Vortex Lattices in Ferromagnetic Superconductors
It has been theorized that in these novel type II superconducting materials, vortex lattices can spontaneuously (i.e. without an external magnetic field) develop. It has been shown (http://link.aps.org/doi/10.1103/PhysRevB.71.224506) that the elastic properties of such vortex lattices are just like those of a columnar liquid crystal. I am planning to study the way in which these types of vortex lattices "depin" (see above).
- Liquid Crystals
I am interested in many different types and aspects of liquid crystals, in particular how they are affected by disorder.
Interested? My interest and research in these areas is theoretical in nature. Students interested in working with me on this should be mathematically proficient. Thermal physics would be useful but is not crucial.
Experimental Liquid Crystal Projects
The Liquid Crystal Institute (http://www.lci.kent.edu/) at Kent State University are helping to facilitate experimental liquid crystal research here at Cal Poly. In particular they have been sending us liquid crystal samples for use in projects.
- Building Liquid Crystal Cells and Observing their Opto-Electical Properties
This ongoing project involves constructing basic liquid crystal cells. Optical techniques are then used to see how light is affected by the liquid crystal cell. The behavior of the liquid crystal under the influence of an externally applied field can also be explored.
YOU can control the experiment online here (http://129.65.36.169/fredtran.html)
- Building Dye Doped Liquid Crystal Cells and Observing their Nonlinear Optical Response
This is an extension of the above project. Liquid crystals can be affected by the electric field of the light passing through them. This can in turn affect the electric field of the light and leads to an optical nonlinearity. Doping the liquid crystal with a dye can dramatically enhance this response of the liquid crystal and can lead to very interesting nonlinear optical effects.
- Ultrasonic Measurements of Liquid Crystals
This project is being supervised by Dr. Matt Moelter and involved measuring the velocity and attenuation of sound passing through liquid crystals. Liquid crystals can be thought of as being anistropic liquids and this anistropy makes there ultrasonic properties very interesting.
Interested? Electronics is a big component in each of these projects so interested students should have taken 206/256.
Miscellaneous Projects
- The Physics of Balancing a Soda Can
In a nice demonstration a soda can containing the right amount of liquid can be balanced on its edge (see figure 1 below). Try it! This ongoing project involves analyzing the physics of this demonstration. While the conceptual physics is straightforward (gravitational torque), it turns out that there is quite a lot going on. So far, this project has been theoretical in nature so far but there are several experimental components that could be explored.
Interested? The theoretical side of this project is quite mathematical. Students interested in working on this should be mathematically proficient and experience with Maple would be useful.
Figure 1: Balancing a soda can
- Nonlinear Dynamics of a Spinning Magnet
This project would be an extension of a lab from Phys 417 (Nonlinear Dynamics). A permanent magnet that is free to spin and is placed between two Helmholtz coils shows some very interesting nonlinear behavior. This behavior can be modeled by a relatively simple nonlinear differential equation that yields complex behavior. In this project would be both theoretical (mathematically modeling the system) and experimental (comparing it to the real system) in nature.
Interested? The theoretical side of this project is will involve numerical simulation of a differential equation and experience with Maple/Matlab would be useful.
