Milos Dolnik
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Education:
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Research Interests:
Nonlinear Chemical Dynamics
My research interests include the study of dynamic behavior of nonlinear
chemical systems. Experimental and numerical studies of chemical oscillating
reactions are performed in well mixed flow-through, semibatch or batch
reactors. Investigations of forced and coupled oscillating reactions are
being conducted. The research concentrates also on the effects of delays
in chemical kinetics.
Pattern Formation in Reaction-Diffusion Systems
When chemical reactions are combined with diffusion, spatial patterns and
waves can be produced. Chemical reaction-diffusion patterns constitute
the most convenient analog models for pattern formation in neurobiology,
morphogenesis, chemotaxis, and ecology. My research program includes: a
search for wave patterns that emerge in uniform stable systems via the
wave bifurcation, spontaneous formation of target and spiral wave patterns
in uniform and nonuniform reaction-diffusion systems and the study of chemical
wave propagation and interaction resulting in new types of pattern formation
in nonuniform media.
Modeling and Analysis of Gene Networks
We model the interactions in gene regulatory networks as biochemical reactions and
analyse their dynamics. The existence of positive or negative feedbacks in gene networks
lead to nonlinear rate equations and methods of analysis of nonlinear chemical systems
are used to study dynamics of both synthetically engineered gene networks and naturally
occurring gene networks.
Cell Cycle Dynamics
Using mathematical modeling of cell division cycle dynamics, we have studied a potential
mechanism for controlling the frequency of cell division cycle. Control of the cell cycle is
achieved by artificially expressing a protein that reversibly binds and inactivates one of the
cell cycle proteins. In the simple case of the checkpoint-free situation, encountered in early
amphibian embryos, the frequency of cell cycle oscillations can be increased or decreased by
regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein.
Deterministic Chaos
Deterministic chaos is characterized by long-term unpredictability arising
from an extreme sensitivity to initial conditions. Investigations are being
conducted on emergence of chaos in chemical systems. Extended calculations
are being performed on coupled chaotic systems to see under what conditions
a pair or group of chaotic oscillators exhibits periodic or even steady
state behavior. The study on coupled chaotic systems could be of considerable
importance for the control and increased efficiency of industrial processes.
It appears that a number of such processes behave chaotically and that
this chaos can result in unpredictable and undesirable low yields.
Control of Chaos and Communication with Chaos
The sensitive dependence characteristic of chaos is advantageous for building
a control system in which a small deliberate perturbation can have a large
response. We demonstrate the possibility that information can be encoded
into chaotic oscillations of the Belousov-Zhabotinsky reaction. The encoding
technique is based on controlling the chaotic oscillations by applying
small parameter perturbations and on learning the grammar of corresponding
symbol dynamics produced by the free-running chaotic system. The encoding
technique can be easily utilized for targeting and stabilization of any
unstable periodic orbit.
Mathematical Modeling of Complex Chemical Reactions
Modeling of complex chemical reactions is performed for well mixed and
distributed systems using solvers for integrating stiff ordinary and partial
differential equations. Continuation of stationary and periodic solutions
reveals bifurcation, multiplicity and stability of solutions. Statistical
analysis (e.g. Fourier spectra) is used to characterize the numerical and
experimental data.