Soumyajit Mandal
Bio [2008]
Soumyajit Mandal is a graduate student at MIT in
electrical engineering and computer science. One of his
main interests is novel ways of performing computation, particularly
in biological systems and using distributed active media. Currently he is
working on circuits that emulate the spectral decomposition of
sound in the cochlea (inner ear), but at radio frequencies instead of
audio. He is also doing some work on hardware models of biochemical
networks. In the past he has worked on communication systems using
chaos, analog, mixed-signal and RF circuit design, biomedical systems,
and antennas.
Project Title
Exploring Nonlinear Partial Differential Equations
Project
This project is to find partial differential equations (PDEs) that can
be implemented in some physical medium and used for fast distributed
computation. An example is the spatially varying wave equation that is
used by the mammalian cochlea to decompose input sounds into their
constituent frequency components. Nonlinear PDEs of the first and
second order will be investigated, beginning with those that have two
independent variables (one space and one time dimension). A good
example is the wave equation (an example
of bizarre behavior exhibited by a nonlinear wave equation may be
found on pages 165 and 166 of the NKS book). Hyperbolic equations like
the wave equation have the nice property that information only travels
at a given finite wave speed, meaning that specifying initial
conditions is sufficient for finding solutions at later times. Other
boundary conditions can be largely ignored. Another class of systems
that will be looked at is reaction-diffusion equations with
three or more variables, which appear to have received relatively
little attention but are known to be capable of generating a wide
range of complex spatio-temporal patterns.
The main reason nonlinearities are important is that they are unavoidable
when there are any active processes in the system. Active
processes, which require energy inputs to function, are necessary in order
for any PDE to be used for computational purposes: a simple passive system
is basically dead and decays to equilibrium in an uninteresting way. The
goal is to discover interesting PDE behavior by adding simple generic
nonlinearities of various types to hitherto linear equations, group these
behaviors into classes, and then analyze them.
Project Demonstrations
A Passive Cochlear Model
Distribution of the
Last Digit of the Primes
Favorite Radius 3/2 Rule
Rule chosen: 43371
This is rule 43371 run for 200 steps with random initial conditions. I
like it because for most initial conditions it produces strange biphasic
behavior where different types of randomness appear on either side of an
irregular boundary. Because I am an astronomy enthusiast, this boundary
also reminded me of the day-night terminator on a cratered surface like
the moon.
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