Sharif Digital Repository

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first-order approximation, the method reduces to a linear eigen-value problem which is solved using standard numerical methods. I apply the method to the dynamics of a model stellar disk which is embedded in the field of a soft-centered logarithmic potential. The outcome is the full spectrum of eigen-frequencies and their conjugate normal modes for prescribed azimuthal wavenumbers. The results show that the fundamental bar mode is isolated in the frequency space, while spiral modes belong to discrete families that... 

We present N-body simulations of unstable spiral modes in a dynamically cool collisionless disc. We show that spiral modes grow in a thin collisionless disk in accordance with the analytical perturbation theory. We use the particle-mesh code SUPERBOX with nested grids to follow the evolution of unstable spirals that emerge from an unstable equilibrium state. We use a large number of particles (up to N = 40 & 106) and high-resolution spatial grids in our simulations (1283 cells). These allow us to trace the dynamics of the unstable spiral modes until their wave amplitudes are saturated due to nonlinear effects. In general, the results of our simulations are in agreement with the analytical... 

In this paper, a nonlocal elasticity formulation is presented for analyzing the instability of nano-peapods by modeling the nanotube as a shell. Using the nonlocal elasticity theory, the small scale characteristics of Carbon Nano-Peapods (CNPs) are taken into account. While the classical elastic shell model overestimates the critical pressure for the onset of structural instability of carbon nanotubes, the obtained results show that the nonlocal elastic shell model for nano-peapods can potentially provide better predictions. According to the results, it is concluded that the presence of C 60 inside (10,10) Carbon Nanotubes (CNTs) significantly increases the stability resistance of the single... 

The stability of single-walled carbon nanopeapods under hydrostatic pressure is investigated using a continuum-based elastic shell model. The model incorporates nonbonded van der Waals interactions between the nested fullerenes and the host carbon nanotube. By deriving an explicit equation, it is shown that the critical hydrostatic pressure for the onset of structural instability of a completely packed C60@(10,10) nanopeapod is ∼1.11 GPa, while for the case of the pristine host (10,10) nanotube it is ∼1.84 GPa. Thus, it is concluded that the fullerene encapsulation weakens the host nanotube under hydrostatic pressure. In addition, it is quantitatively shown that any decrease in packing... 

The atomic structure of metallic glasses (MGs) plays an important role in their physical and mechanical properties. Numerous molecular dynamics (MD) simulations have been performed to reveal the structure of MGs at the atomic scale. However, the cooling rates utilized in most of the MD simulations (usually on the order of 109-1012 K/s) are too high to allow the structure to relax into the actual structures. In this study, we performed long-term pressurized sub-Tg annealing for up to 1 μs using MD simulation to systematically study the structure evolution of Cu50Zr50 MG. We find that from relaxation to rejuvenation, structural excitation of MGs and transition during sub-Tg annealing depend on... 

The structural instability of an array of cantilevers, each of which interacts with two neighbouring beams through electrostatic and van der Waals forces, is studied. Distributed and lumped parameter modelling of the array result in a set of coupled nonlinear boundary value problems and a set of coupled nonlinear equations, respectively. These coupled nonlinear systems are solved numerically for different numbers of beams in the array to obtain the pull-in parameters. The pull-in parameters converge to constant values with an increase in the number of beams in the array. These constants, which are important in the design of cantilever arrays, are compared for the distributed and lumped... 

In this paper, combined effects of material degradation, p-delta, and foundation uplift are incorporated in a soil-structure-interaction (SSI) framework to assess seismic response of a single-degree-of-freedom system. The considered phenomenological systems represent a column with a lumped mass on top is placed on a rigid foundation. The foundation is mounted on Winkler springs and dashpots to take account of soil-foundation compliance and material/radiation damping. The springs are tensionless to guarantee that uplift is properly modelled. The model is verified for two specific limit cases with the code and literature to make sure that the model is capable of capturing SSI and foundation...