Professor Ramkrishna’s research group is motivated by ideas in the application of mathematics to solving problems in chemical and biochemical reaction engineering. Such problems involve both model building towards capturing essential behavior of systems, and evolving the theoretical and experimental machinery for the identification of model parameters and phenomenological functions. Their research ideas arise from linear (operator methods) and nonlinear analysis of ordinary and partial differential equations, stochastic processes, and population balance modeling involving integro-partial differential equations. The major thrust is fundamental and inspired generally by key technological issues. Our focus is on problems associated with the production and conservation of energy.
Chemical Reaction Engineering
Research emphasis in reaction engineering is on orchestration of interfacial mixing and reaction to promote selectivity and conversion in heterogeneous reactors. Bubble column reactors have been of interest in the past in collaborative research with Professor J. B. Joshi of Mumbai University Institute of Chemical Technology. Future interests are in modeling Fischer-Tropsch synthesis reactors. Current interest in reaction engineering, however, has been focused on metabolic systems. Multiple steady states, predicted by bifurcation analysis of hybrid cybernetic models, are under experimental investigation for feeds to continuous reactors of mixed substrates containing glucose and pyruvate. Also of interest are conditions for periodic behavior. Such nonlinear behavior not only has its usual significance to chemical reactor behavior as in the past but of fundamental importance to whether regulatory behavior of biological systems are properly represented by cybernetic concepts. Top
Dispersed Phase Systems
The research focus in this area is in two areas. The dynamic modeling of the evolution of crystal morphology distributions is under investigation in crystallizer environments in collaboration with Dr. Steef Boerrigter and Professor Kai Sundmacher of the Max Planck Institute in Magdeburg, Germany. The collaboration has been extended to Mumbai University with Professor J. B. Joshi through a grant from the Department of Science and Technology, India for investigating large crystallizers in which mixing effects are modeled by using computational fluid mechanics.
A second area of interest is in the modeling of milling operations in the pharmaceutical industry as part of the NSF Engineering Research Center thrust. The use of population balances and Markov chains is being investigated for identification of transition probability matrices from observed dynamics of particle size distribution accounting for segregation and limited mixing for both linear and nonlinear breakage.
Active investigation of dynamic cybernetic models is in progress for various applications. Thus current activities include metabolic modeling of yeast, bacteria and cyanobacteria in collaboration with Professor John Morgan, and Professor Lou Sherman of Purdue Biological Sciences. Metabolic engineering interests include improved production of biofuel productivity and the production of hydrogen from cyanobacteria. Also under investigation are fundamental aspects of biological robustness from the cybernetic point of view.
In a collaborative project with Minnesota supported by NIH, we are investigating pheromone-induced transfer of antibiotic resistance by bacteria. This project involves modeling of gene-regulatory processes from the perspective of stochastic population balance analysis of protein synthesis in signal transduction pathways.
Specific applications drive research effort in applied mathematics generally from the areas of linear operator theory, stochastic processes and the solution of inverse problems. With Professor Osman Basaran, we are involved in an investigation of surface oscillations of drops supported on orifices and holes of finite thickness.
The research focus here is diverted into two areas. First, dynamic mathematical models and systems engineering principles are exploited to solve some of the long standing problems in Cancer treatment. Efforts are underway to develop a model-based clinical decision support tool to assist physicians in treating Leukemia patients. The tool will incorporate genetic and other treatment related variations among patients and predict the future course of response for a given treatment. In addition, one can determine optimal dosing profile according to patient’s characteristics.
A second area of interest is in identifying novel biomarkers for early detection of chemotherapy-induced peripheral neuropathy. Using pharmacometabonomics approach, efforts are in progress to establish connection between endogenous metabolites and neuropathy observed during Vincristine treatment. Both the works involve collaboration with Physicians at Riley Hospital for Children, Indianapolis.