Sharif Digital Repository

We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a longrange attractive and a short-range repulsive potential field known as Morse potential. We assume Stokesian drag force between particles and their carrier fluid and find analytic single-peaked traveling solutions for the spatial density of particles in the catastrophic phase. In steady flow conditions the streaming velocity of particles is identical to their carrier fluid, but we show that particle streaming is asynchronous with an unsteady carrier fluid. Using linear perturbation analysis, the stability... 

We use coarse grained molecular dynamics simulations to investigate diffusion properties of sheared lipid membranes with embedded transmembrane proteins. In membranes without proteins, we find normal in-plane diffusion of lipids in all flow conditions. Protein embedded membranes behave quite differently: by imposing a simple shear flow and sliding the monolayers of the membrane over each other, the motion of protein clusters becomes strongly superdiffusive in the shear direction. In such a circumstance, the subdiffusion regime is predominant perpendicular to the flow. We show that superdiffusion is a result of accelerated chaotic motions of protein-lipid complexes within the membrane voids,... 

We investigate the stability of the pressure-driven, low-Reynolds-number flow of Brownian suspensions with spherical particles in microchannels. We find two general families of stable/unstable modes: (i) degenerate modes with symmetric and antisymmetric patterns; (ii) single modes that are either symmetric or antisymmetric. The concentration profiles of degenerate modes have strong peaks near the channel walls, while single modes diminish there. Once excited, both families would be detectable through high-speed imaging. We find that unstable modes occur in concentrated suspensions whose velocity profiles are sufficiently flattened near the channel centreline. The patterns of growing unstable... 

We carry out a coarse-grained molecular dynamics simulation of phospholipid vesicles with transmembrane proteins. We measure the mean and Gaussian curvatures of our protein-embedded vesicles and quantitatively show how protein clusters change the shapes of their host vesicles. The effects of depletion force and vesiculation on protein clustering are also investigated. By increasing the protein concentration, clusters are fragmented to smaller bundles, which are then redistributed to form more symmetric structures corresponding to lower bending energies. Big clusters and highly aspherical vesicles cannot be formed when the fraction of protein to lipid molecules is large  

Macroscale experiments show that a train of two immiscible liquid drops, a bislug, can spontaneously move in a capillary tube because of surface tension asymmetries. We use molecular dynamics simulation of Lennard-Jones fluids to demonstrate this phenomenon for NVT ensembles in submicron tubes. We deliberately tune the strength of intermolecular forces and control the velocity of bislug in different wetting and viscosity conditions. We compute the velocity profile of particles across the tube and explain the origin of deviations from the classical parabolae. We show that the self-generated molecular flow resembles the Poiseuille law when the ratio of the tube radius to its length is less... 

We use the weighted integral form of spherical Bessel functions and introduce a new analytical set of complete and biorthogonal potential-density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to r-(1+ l) and r-(4+ l) at large radii, where l is the latitudinal quantum number of spherical harmonics. The lowest order term associated with l = 0 is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modelling of three-dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our... 

A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of spherical Bessel functions. We discuss on the properties of our basis functions and demonstrate their shapes for the latitudinal Fourier number l = 2. © 2008 Copyright International Astronomical Union 2008  

We use a third-order perturbation theory and Melnikov's method to prove the existence of chaos in spinning circular disks subject to a lateral point load. We show that the emergence of transverse homoclinic and heteroclinic points lead, respectively, to a random reversal in the traveling direction of circumferential waves and a random phase shift of magnitude π for both forward and backward wave components. These long-term phenomena occur in imperfect low-speed disks sufficiently far from fundamental resonances. © 2007 American Institute of Physics  

We present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed physical quantities in terms of a complete basis set and a small non-axisymmetry parameter e. We then derive a linear eigenvalue problem in matrix form, and determine the pattern speed, growth rate and mode shapes of the first three unstable modes. In non-axisymmetric discs, the amplitude and the phase angle of travelling waves are functions of both the radius R and the azimuthal angle φ. This is due to the interaction of different wave components in the... 

We report the existence of interfacial instability in the two-dimensional channel flow of a sediment suspension whose particles diffuse in the carrier fluid due to shear-induced collisions. We derive partial differential equations that govern the deformations of the interface between the sediment suspension and the clear fluid, and devise a perturbation method that preserves the positivity of the particle volume fraction. We solve perturbed momentum, particle transport and deforming interface equations to show that a Kelvin-Helmholtz-type unstable wave develops at the interface for wavelengths longer than a critical value. Short-wavelength oscillations of the interface are damped due to... 

Protein aggregation in cell membrane is vital for the majority of biological functions. Recent experimental results suggest that transmembrane domains of proteins such as α-helices and β-sheets have different structural rigidities. We use molecular dynamics simulation of a coarse-grained model of protein-embedded lipid membranes to investigate the mechanisms of protein clustering. For a variety of protein concentrations, our simulations under thermal equilibrium conditions reveal that the structural rigidity of transmembrane domains dramatically affects interactions and changes the shape of the cluster. We have observed stable large aggregates even in the absence of hydrophobic mismatch,... 

Modern sensors consist of arrays of detectors specially arranged to enhance precision, capabilities, and field of view (FOV). Sensor arrays can have multiple functionalities, such as the simultaneous detection of position and motion. We use a linear sensor model and develop an optimization method to design an array of photodiodes. Our objective function minimizes bias and variance estimations. We introduce a maximum likelihood technique to approximate and determine the bias caused by measurement errors, and verify our theory by statistically complete simulations. We apply our theory to design an optimal sun sensor. The sensor has a predefined conical FOV, and its accuracy is controlled by a... 

This research is dedicated to show the possibility of using solar radiation pressure by solar sails for interplanetary flights. In this paper, in addition to the Introduction of solar sailing and physics of solar radiation pressure, the solar sail orbital dynamics for optimal trajectory of an ideal solar sail spacecraft has been studied. It considers the problem of optimal controlling the sail angle so as to execute a minimum-time coplanar orbit transfer from the circular initial orbit to the circular target orbit. The direct collocation optimal control technique is used to transform the state equations to a set of nonlinear algebraic constraint equations. The results of state and control... 

Three-dimensional orbits in the vicinity of the collinear libration points of the Sun-Earth/Moon barycenter system are currently being considered for use with a number of missions planed for 2000 and beyond. Since such libration point trajectories are, in general, unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. In this paper, circular restricted three body problem is reviewed and a numerical method to control spacecrafts on periodic halo orbits around L1 and L2 collinear points of the Sun-Earth/Moon barycenter system is investigated. The control approach is based on the optimal control theory and implements variation... 

We report the design, fabrication and error analysis of a sun sensor array composed of six photodiodes. The sensor estimates the direction of the sun using a linear least squares method. The performance of the sensor is deteriorated by three major sources: fabrication errors, scattered environmental light, and inexact modeling of photodiodes. Using a calibration procedure and modeling the uniform component of the environmental light, we mitigate the first two errors and significantly reduce root mean squared error from 2.63° to 0.83°. For a Field of View (FOV) of 110°, the maximum estimation error also drops from 3.8° to 1.6°. Through exact mathematical modeling of photodiodes, we... 

Several semi-analytical models are considered for a double-gyre problem in a turbulent flow regime for which a reference fully numerical eddy-resolving solution is obtained. The semi-analytical models correspond to solving the depth-averaged Navier–Stokes equations using the spectral Galerkin approach. The robustness of the linear and Smagorinsky eddy-viscosity models for turbulent diffusion approximation is investigated. To capture essential properties of the double-gyre configuration, such as the integral kinetic energy, the integral angular momentum, and the jet mean-flow distribution, an improved semi-analytical model is suggested that is inspired by the idea of scale decomposition... 

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... 

Due to inherent potential of General Regression Neural Network(GRNN) to approximate nonlinear functions, it can be implemented as a nonlinear state-feedback controller. In this paper the methodology of direct collocation and nonlinear programming is utilized in combination with GRNN to determine the optimal control of dynamical systems. Application of this method to the design of an optimal controller for a chaotic flexible beam as a non-autonomous, nonlinear system is investigated. © 2002 The American Institute Aeronautics and Astronautics Inc. All rights reserved