Critical Phenomena and Boiling
Fluid dynamics is a topic that I have been working on since 2001. I am particularly interested in developing two research directions:- experimental approach on fluid instabilities, and
- numerical methods for investigating the turbulent flows inside fluids.
The rectangular geometry of the fluid cells heated from bellow is used to investigate all sorts of nonequilibrium processes from Rayleigh-Benard to Taylor-Couette instabilities. Optical methods were previously limited to identifying the convective structure, and used of linear methods in frequency domain to extract characteristic length and correlation features from recorded images. I previously used a fluid cell with cylindrical symmetry and measured optical properties along the main axis. However, the method records only two dimensional snapshots of fluctuations and contains no information regarding the bulk distribution of observed changes in fluid's density. I intend to redesign the experimental cell such that I can acquire additional information by simultaneously recording two dimensional snapshots of fluctuation perpendicular to the main axes of the cylindrical cell. The method I intend to use for reconstruction of three dimensional image of the fluid cell from two dimensional pictures is based on recursive matching of the correlation structure of bulk fluctuations model and the two dimensional experimental snapshots. Based on the three dimensional computer representation of fluctuations inside the fluid we will have a between understanding of the specific interfacial forces involved in heat flow transport. This refinement in the experimental procedure is necessary in order to distinguish what fraction of the currently classifies gas-fluid-solid interfaces are actually two-phase interfaces, such as gas-fluid or gas-solid. I would also like to study the fluid instabilities using spherical geometry with direct applicability to turbulences and weather patterns. One possible experimental setup that I already tested during my graduate studies consists in a immersing a metallic sphere in a dielectric fluid such as silicon oil and encapsulate the whole system in a transparent spherical shell centered in the metallic sphere. Turbulences and large-scale convectives (hurricanes) were experimentally observed due to applied thermal gradients between the inner metallic sphere and the outer shell I intend on developing both the experimental setup and implement a computational model for spherical geometry.
Image Processing
Image processing is one of the fastest growing research field related to nondestructive and noninvasive techniques. Optical information carries important hints regarding physical processes inside of remote and/or inaccessible objects. My primary research interest in this field is to implement computer models for feature extraction from two dimensional snapshots. Traditional image processing tools for image enhancement and noise reduction use filtering methods both in temporal and frequency domains. Based on my experience with images analysis of fluctuations in fluids near the critical point, I would like to continue working on improving existing techniques and developing new quantitative measures for both spatial and temporal organization. We previously found that the histogram and the radial average of the power spectrum can be successfully used to estimate thermodynamics properties of transparent fluids. I would like to refine the image processing method in order to extract also information about dynamical processes such as heat transfer and other convective flows by combining two dimensional snapshots with computer reconstruction of three-dimensional objects.
Theoretical Condensed Matter
In their 1987 work, Bak, Tang and Wiesenfeld showed that certain open, dissipative, spatially extended systems spontaneously achieve a critical state characterized by power-law distribution of event sizes. They called this phenomenon Self-Organized Criticality (SOC) and illustrated it using a simple two-dimensional cellular automaton model for sandpiles. Since then, many natural phenomena have been connected to SOC, including but not limited to earthquakes, evolution, interface dynamics, vortices in superconductors etc. Nonequilibrium surface growth and interface dynamics represent an effervescent area of research with a large number of discrete atomistic growth models and stochastic growth equations exhibit generic scale invariance characterized by power law behavior (SOC). Diffusion Limited Aggregation (DLA) is the main paradigm used to solve the aggregation of clusters via diffusion and attachment. Electrochemical deposition and Molecular Beam Epitaxy are two examples of general models developed in the context of DLA and implemented using cellular automata algorithms. Molecular Beam Epitaxy is applied, for example, in the growth of layered semiconductor heterostructures for electronic devices or in the development of thin magnetic films for novel storage media, which also plays a significant role as a tool in the design of nanostructures, such as Quantum Wires or Dots. The computation I developed for DLA modeling incorporates the traditional Metropolis-updating rule subject to detailed balance. The novelty of the proposed approach consists in connecting the macroscopic measures, such as surface roughness, to dynamic quantities, such as the exponent of the two-particle interaction potential. Our preliminary results indicate a deterministic relationship between the capacity fractal dimension and the exponent of the two-particle potential. Therefore, our method could be used in conjunction with the electron microscopy to determine the Hamiltonian at the microscopic level. I intend to extend the applicability of the method for the purpose of microscopic model prediction by including higher order fractal measures. Of special interest is also the development of numerically efficient implementation of the DLA cellular automata. The initial implementation used Pascal (because of the integrated graphic interface that allows instant graphic visualization of numerical results). More recently the whole implementation was ported to the C language (for fast computation) and interfaced with Mathematica (for easy graphical visualization).
Use of Technology in Classroom
I am a firm believer in the need for efficient teaching. In the recent decade, the advances in technology and the wide spread of computers have introduces new means for teaching. However, most of these techniques are used inefficiently and usually do not result in improved class outcome. My research interests here are related to the study of linking class presentation and assessment tools to classic educational methods. My research in this field materialized in three books designed to help students enhance their conceptual understanding of physics principles and strengthen their problem solving skills. I am currently developing a set of conceptual problems to be used in conjunction with the "peer instruction" method.