| Unstable Disk Galaxies:
Spiral Structure Formation. Since
2003, I have been investigating the unstable modes of stellar disks and
the formation of spiral structure. This problem has a long history
dating back to early 1960s. However, most available numerical methods
developed so far cannot unveil the full modal spectrum of disk
galaxies. I developed a new weighted residual method for
computing the unstable and van Kampen modes of disk galaxies, and
classified their eigenspectra. I suggested a new dynamical mechanism
that triggers
unstable modes of stellar disks: capture of stars into resonance by
randomly
generated waves near the corotation. My theory predicts the saturation
of growing waves in
the nonlinear regime when the corotation resonances of two neighboring
modes compete to capture certain groups of stars. |
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| Protein Dynamics in Lipid Membranes.
One of my new research areas, which is currently pursued
with the help of Amir Houshang Bahrami (Ph.D. student), Atefeh
Khoshnood (Ph.D. student) and Maziar Heidari (M.Sc. student) is the
dynamics of lipid membranes and
vesicles. We intend to understand how transmembrane proteins influence
the mechanical properties of a membrane (vesicle). Of great importance
is to make a general shape classification of vesicles under a variety
of dynamical interactions and initial conditions. |
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| Space Observatory
Simulator. Some engineered systems in outer space remain
unreachable even by their designers and operators. It is therefore
important to understand their dynamics and find a way to simulate them
in Earth-based laboratories. Of
particular interest to astronomers is the re-orientation of
space
observatories in search of their to-be-observed stars, galaxies,
clusters and interstellar media. We (Mohsen Saadat, M.Sc. Thesis; Mir
Abbas Jalali, supervisor) have designed, and prototyped a simulator for
three-dimensional maneuvers of a model observatory. We are
using a combination of
angular-momentum-storage wheels and stepper
motors to re-orient a levitated spherical body so that its vision
system smoothly
(and continuously) tracks a light source (star). |
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| Chaos in the Roto-Translatory Motion of Rigid Bodies. Natural satellites in the solar system have complex dynamics. They are usually triaxial (with no symmetry axis) and undergo a roto-translatory motion. The rotation of the Moon is an example of such complex phenomena. We have attempted to explore the phase space of triaxial moons while they orbit around their mother planets on elliptical orbits. We have identified chaotic layers and measured the variation of the Kolmogorov-Sinai entropy versus a triaxiality parameter. We have also found a new set of stable periodic configurations that may have engineering applications. |
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| Nonlinear Oscillations of Hard Disk
Drives. Hard disk drives (HDDs) are among the most important
and sensitive components of computers. They are indeed spinning disks
with layers of magnetic material and coated by hydrogenated amorphous
carbon. The read-write head flies over the spinning disk due to the
aerodynamic force and digital information is written/read on/from the
disk by the Leaked Magnetic Field/Giant Magnetoresistivity. The air gap
between the head and the disk is a crucial parameter that guarantees a
reliable exchange of data, and the data access rate is directly
proportional to the spin rate. However, undesired transverse
oscillations of the
disk, due to external shocks (mostly in laptops) and the lateral
aerodynamic force of the head, constrain the angular velocity of the
disk (which limits the data access rate) and cause abnormal variations
of the nanoscale air gap. In our research group, we have worked on
different
models of hard disk oscillations and calculated corresponding
eigenmodes (in collaboration with Atefeh Khoshnood and Saeid Dousti).
We have shown that hard disk oscillations can become
chaotic by two major mechanisms: (i) destruction of invariant manifolds
in imperfect disks (ii) modal interactions in nonlinear regime (in
collaboration with Arzhang Angoshtari and Majid Rajabi). We are
currently working on the application of circumferentially re-inforced
composite materials in the next generation of HDDs. Our preliminary
results show
that composite disks allow for larger angular velocities, and
therefore, data access rates. |
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