It is noticed that science develops in splashes, changing our outlook. 19th century was the time of rapid development of thermodynamics and electrodynamics; in the beginning of the 20th century quantum mechanics and relativity were born. Now we seem to be at the dawn of efflorescence in nonlinear science and the study of complex systems. These systems are now identified in nearly all areas of science: information theory, biology, condensed matter physics, electronics, astrophysics, and so on.
I became interested in science when I was a high school student. Physics, Biology and Chemistry were fields of my special interest. I realized that one who wants to become a scientist must have not only an excellent grounding in theory but also wide research experience. At that time I became interested in nonlinear phenomena in biophysics. I worked with a group of high school students studying propagation of nerve impulse under the effect of high concentrations of detrimental compounds. As a result, we prepared a report to the all-Ukrainian high-school students Physics Conference. Simplicity and clarity of designed physical model along with importance and originality of the obtained results impressed me greatly.
My interest in nonlinear systems appeared when I was a first year student at Kiev University. Under the supervision of Dr. A I set about research on the characteristics of chaotic oscillations in Kiyashko-Pikovsky-Rabinovich generator. Our goal was to simulate oscillations produced by the system under different conditions and to modify the theory explaining statistical properties of oscillations produced in the studied regimes. Soon I developed computer simulation of the system. After a short period of investigations we discovered several new types of behavior of the generator. Lamerey's diagrams and phase-plane portraits were constructed for each new regime. From these results we reconstructed the overall bifurcation sequence leading to stochastic regimes and regions of parameter space, where the different types of oscillations exist. Results of the work were published in the Bulletin of Kiev University as well as presented at MIPT Scientific Conference and all-Ukrainian Student Scientific Conference.
After transferring to MIPT I started studies in nonlinear quantum optics. I took advanced theoretical and laboratory courses on the subject. In 1999 I began to work as a research assistant in Dr. Bs laboratory in Lebedev Physics Institute, Moscow. Along with two other MIPT students, I designed an arrangement for generation and detection of light with hidden polarization. Our ultimate goal was further improvement of squeezed light characteristics produced by parametric generator. As a part of the work I studied chaotic behavior of this system. This research gave me the extensive experience, since I had to familiarize myself with different aspects of theoretical, experimental and computational techniques. Later I found another application of optical systems with chaotic behavior while working on dynamics based computation project with Prof. C.
Last year I became interested in interconnection between chaos and information theory and joined Prof. Cs research group, which works in the field of information and communication technologies based on dynamical chaos. At the same time I took several courses on nonlinear dynamics, chaos, complexity and theory of self-organization. My first research project was Dynamics Based Computation. Plenty of information that I learned while working on it improved my understanding of such phenomena as self-organized criticality and information processing by chaotic map. Currently I am engaged in research on Chaotic Map based Associative and Random Access Memory. We have already designed Matlab program that records multiple text strings on one chaotic map and then identifies and restores recorded string on the basis of its substring. Now I am working on improvement of the effectiveness of this model.
I started my teaching practice as soon as I entered Kiev University in 1997. I conducted additional physics studies for gifted high school students in Ukrainian Lyceum of Physics and Mathematics in Kiev. I enjoyed this kind of work greatly so after transfer to MIPT I joined Prof. D's group that provides trainings for Russian International Physics Olympiad Team. This experience has convinced me that I would enjoy simultaneous teaching and research in the case of having TA position.
In the summary, my interest lies in the field of nonlinear dynamics and its applications, namely nonequilibrium physics, complex systems, self-organization, dynamics of neural networks. Research in this areas is very active at California Institute of Technology, namely at Physics, CNS, CDS and other departments. Therefore I want to continue my education at California Institute of Technology. I am sure that your PhD program will finally lead me to my dream discovering of a secret of nature.