Mark Edelman’s Statement of Research Interests
In 1982 at the department of
Astrophysics of the
from MIT and published in “The Astrophysical Journal” in 1986. Bertschinger’s article was cited almost one hundred times. My publication gave me an opportunity to communicate with astrophysicists from Pulkovo observatory and Ioffe Physico-Technical Institute.
The next natural step was to
consider the corrugation instability of magnetized radiative and adiabatic
shocks, as the astrophysical plasma, especially for the case of the accretion
onto magnetized stars, is always magnetized. As the result, the whole linear
theory of corrugation instability of radiative and magnetized gases was
created. I ended my work on this theory in 1995 with the work done in
collaboration with James Stone from
In 1995 George Zaslavsky offered me to work on the computer simulations related to chaos theory at the Courant Institute. I accepted this offer and since 1995 the chaos theory has been the subject of my research. Particular areas of my interest include research on the connection between topological properties of phase space of dynamical systems and transport coefficients, pseudochaos (with zero Lyapunov exponent), description of dynamical systems by fractional differential equations and numerical solution of such equations. Design of corresponding software (visual C++) and web design are just hobbies. An application Phase Portrait Builder can be sent upon request and I can issue a password for my educational site: http://cims.nyu.edu/~edelman/MyCourse/Precalculus0/Precalculus/
In their pioneering work Nick Laskin and George Zaslavsky (Physica A, 2006) showed that systems of long range interacting oscillators in the infrared limit (small k) can be adequately described by fractional partial differential equations. This work stimulated activities in our group related to generalization of the properties of well known PDEs like sine-Gordon equation, non-linear Shrödinger equation, Ginzburg-Landau equation etc. for the case of fractional space derivatives. This is also the area of my main interest at the present time.