Sharif Digital Repository

The Liouville equation for the distribution function is solved and a series solution for the Wigner distribution function is derived. In this solution, potential is nonlocal so that the distribution function in each point is influenced by the potential of the entire space. By computing the carrier density, an effective classical potential is defined. In a quantum system this effective potential replaces the classical potential. Based on the solution of the Liouville equation a novel set of three-dimensional quantum hydrodynamic equations (QHD) is derived. The form of the resulting QHD equations is similar to the classical hydrodynamic (HD) equations but there are explicit quantum corrections... 

We study the formation of a vortex with fourfold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observe five other regimes in the system: a homogeneous gaseous phase, band structures, moving clumps, moving clusters, and vibrating rings. All six regimes emerge from controlling the strength of noise and from the contribution of repulsion and alignment interactions. We study the shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion... 

Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is... 

A new discretization scheme for the current density in the hydrodynamic model is presented. This scheme is an extension of the Scharfetter-Gummel (S-G) method and is derived without neglecting the convective term in the current density. Simulation of two model n-i-n diodes shows that this method gives better numerical results than the conventional upwind and S-G methods. © 2004 Elsevier B.V. All rights reserved  

In this work, a hybrid finite-volume-element method is used to solve turbulent reacting flow in a combustion chamber considering detailed chemical kinetics. The hybrid unification enables the solver to treat the reacting flow in very complex geometries and to respect the required physical considerations fully. We employ two-equations standard κ-ω turbulence model incorporated with suitable wall functions to model the turbulence behavior. Assuming optically-thin gases, radiation effects are taken into account in our simulations. A flamelet combustion model is applied to consider the large detailed chemical kinetics, which can normally occur within combustion processes. Turbulence-chemistry... 

Mesoscopic hydrodynamic equations are solved to investigate late-stage evolution of thin liquid films over step topographies. Different geometrical parameters including step height and initial position and configuration of resultant masses of dewetting (droplets) are probed to find their effects on the mass evolution of the system. Our results indicate that increasing the step height and locating the droplets close to the step enhance the dynamics and accelerate smaller droplet collapse  

Mesoscopic hydrodynamic equations are solved to investigate coarsening dynamics of two interacting nanodroplets on chemically patterned substrates. The effects of different parameters such as the surface chemical pattern, the slip length, the profile of the disjoining pressure, the size of the droplets, and the contact angles on the coarsening are studied. Our results reveal that the presence of a chemical heterogeneity can enhance or weaken the coarsening dynamics depending on the pattern type and positions of the droplets on the substrate. Also increasing the contact angles to values larger than a critical value may qualitatively change the coarsening process, and the profile of the... 

Due to its rotation, Earth traps a few equatorial ocean and atmospheric waves, including Kelvin, Yanai, Rossby, and Poincaré modes. It has been recently demonstrated that the mathematical origin of equatorial waves is intricately related to the nontrivial topology of hydrodynamic equations describing oceans or the atmosphere. In the present work, we consider plasma oscillations supported by a two-dimensional electron gas confined at the surface of a sphere or a cylinder. We argue that in the presence of a uniform magnetic field, these systems host a set of equatorial magnetoplasma waves that are counterparts to the equatorial waves trapped by Earth. For a spherical geometry, the equatorial... 

In this work propagation of a high frequency electromagnetic wave in underdense plasma in presence of an external magnetic field is investigated. When a constant magnetic field perpendicular to the motion of electrons is applied, then the electrons rotate around the magnetic field lines and generate electromagnetic part in the wake with a nonzero group velocity. By using of the Maxwell equations and nonlinear differential equation for the electric field a direct one-dimensional (1D) procedure for calculating hydrodynamic equations are developed and the electric and magnetic field profiles in the plasma are investigated. It is shown that by using the external (dc) magnetic field in constant...