Sharif Digital Repository

In this thesis , we consider nonnegative (continuous) weak solutions of the porous medium equation with source , u_t-∆u^m=u^p, and p>m>1 .
Assume that, m>1 and 1< p/m u_t-∆u^m=u^p,xϵR^n ,tϵR
has no nontrivial, bounded radial solutions u≥0 .
In one space-dimensional, the conclusion of the result mentioned above remains true without the assumption of the radial symmetry. The proof is based on the intersection-comparison arguments , zero number argum- ents and a key step is to show the... 

In this thesis we consider the dynamics of a general predator-prey model which generalizes several known predator-prey, assuming that the intrinsic growth rate of the pray, the predation rate, and the removal functions are given in an unspecified form. Using the Lyapunov method, we derive sufficient conditions for the stability of the equilibria. also, we consider a delayed periodic predator- prey model and sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solutions of the model.

 

The main topic of this dissertation is to find methods for obtaining parametric solutions and linear/nonlinear invariants of Diophantine equations and consists of 4 chapters. The first chapter consists of some introductory discussions. The second chapter begins with a review of linear invariant, U-invariants, covariants and the concept of semi-invariants. The generators of maximum degree 3 for producing all linear invariants are introduced in Chapter 2 as well. Moreover, the relations between 3rd and 4th degree Hilbert invariants in terms of Procesi bases are included in this chapter.In chapter 3, a general conjecture is given to check whether there are finitely many solutions to a... 

The object of this research is modeling, simulation and control of a crystallization process. Population balance equation (PBE) has been used for modeling of such processes. Most of the existing numerical methods cannot solve the general form of PBE in presence of the breakage and agglomeration terms and some others are not suitable for control objectives, because of their intractable CPU time. In this work a new developed numerical method called conservation element and solution element (CE/SE) has been used for solving general form of multidimensional population balance equations. The accuracy and effectiveness of the scheme is demonstrated through computer simulation. According to the... 

The purpose of this study is the implementation of multi-model predictive control (MMPC) approach for the co-polymerization system of methyl methacrylate - vinyl acetate. Simpler development of local models and controllers and also convenience of understanding the model and controller structure are the main reasons for using this approach. In the first step, RGA analysis has been used for pairing input and output variables. Then the performance of PI controller on the system has been investigated. For designing model predictive controller (MPC) the nonlinear model has been linearized at operational point and the controller has been designed in MPC toolbox of MATLAB software R2013a. In the... 

In this thesis, coupled trajectory and attitude control of an exoatmospheric interceptor is investigated. The interceptor is considered to track and intercept orbital targets in its terminal phase using an infrared strapdown seeker. Attitude control system uses its thrusters in order to keep permanently the detector toward the target in both elevation and azimuth directions. Detector is attached to the body. Divert thrusters generate acceleration perpendicular to the longitudinal axis of the interceptor to correct the trajectory. It is assumed that the interceptor has mass asymmetries. Transltional and rotational dynamics are coupled. Therefore, in order to improve the performance of... 

In this paper, the Hopfield neural network models have investigated. Also the similar model with time -varying delays and constant coefficients has considered and with establishing some criterions, existence solution and it's exponential stability of the solution is investigated. Moreover, some special conditions for exponential stability by impulses and exponential stability by periodic impulses are obtained  

In 1952, Choquet-Bruhat proved the well-posedness of the Cauchy problem for Einstein’s equation, and demonstrated that a given initial data on a Cauchy hypersurface in spacetime propagates forward in time as a solution to the wave equation. It took nearly half a century for mathematicians to build the necessary tools and techniques for proving the stability of the most basic solution of Einstein’s vacuum equations (EVE), namely Minkowski spacetime. In 1993, Christodoulou and Klainerman showed the global nonlinear stability of this solution using the concept of a double null gauge. The Schwarzschild solution, introduced by Karl Schwarzschild in 1916 for spherically symmetric spacetimes as an... 

In this thesis we investigating two models of cancer invasion .First, a general mathematical model of cancer invasion is presented. In this model there are three factors: tumor cell, extracellular matrix and enzyme. The model consists of a parabolic partial differential equation (PDE) describing the evolution of tumor cell density , an ordinary differential equation modeling of extracellular matrix and a parabolic PDE governing the evolution of the matrix degrading enzyme concentration. This model is investigated in two special versions for existence and uniqueness of global solutions. In the first model we neglect the remodeling term, this model is named the chemotaxis-haptotaxis model.... 

In this thesis, we consider a system containing fluid equations, structure equations, and equations of these two materials’ common interface in three dimensions and on the regular domains. We suppose that the solid which is described by the Lamé system of linear elasticity, moves inside an incompressible viscous fluid in three dimensions, and the fluid obeys the incompressible Navier-Stokes equations in a time-dependent domain. At the fluid–solid interface, natural conditions are imposed, continuity of the velocities and of the Cauchy stress forces. The fluid and the solid are coupled through these conditions. By this interaction, the fluid deforms the boundary of the solid which in turn... 

This thesis is based on articles [18,15]. Zhao [18] has studied a free boundary problem modeling the growth of tumors with drug application. In this model live cells are two kindes: proliferative cells and quiescent cells. This model consists of two nonlinear second-order parabolic equations describing the diffusion of nutrient and drug concentration, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells. He has proved that this free boundary problem has a unique global solution. Tao and Chen [15] have studied another free boundary problem modelling the growth of an avascular tumour with drug application. The... 

The Iran-China 25-year Cooperation Program on the further economic development particularly energy area signed on 27 March 2021 by Iran, which suffered from many years of political and economic isolation and China, the second global economy. Energy transition is an essential issue in both country's energy systems which calls for a medium energy carrier that will be the natural gas. China is seeking for new natural gas resources in order to achieve its ambitious net-zero goals and Iran has targeted 50% reduction in its energy intensity. The necessity of supplying the natural gas for Pakistan and China through the CPEC (China-Pakistan Economic Corridor) by Iran is an important criterion in the... 

The main subject of this thesis is to improve conventional CFD algorithms applied in numerical simulation of inviscid unsteady flows around moving boundaries with large relative motions, on unstructured grids. All challenges in this regard are reviewed, and appropriate efficient schemes are introduced to address them. A new scheme is presented for valid grid generation during grid movement and is implemented for 2D and 3D problems. Customary three dimensional convergence acceleration techniques such as implicit time stepping and multigriding have been applied. For implicit solution of the flow equations a new algorithm is used. Via a special renumbering algorithm, the approximate... 

The use of clean energy sources has become increasingly popular around the world in recent years. One of the most important of these sources is wind energy. Due to the high wind potential in offshore areas than on land, this study uses the integration of multi-criteria decision-making methods and GIS to identify the best areas for developing offshore wind farms in the Persian Gulf and the Sea of Oman. Criteria applied in this study are divided into two categories: restrictive criteria, such as recommended transportation routes and anchored restricted areas, and technical criteria, such as wind speed and water depth. After removing the inappropriate areas using restrictive criteria, the... 

Sustainable agricultural development in the country without regard to water supply problems in terms of time and place is not possible. Construction of water storage tanks filled with water and seasonal use in dry seasons in the effective action in the optimal use of water in the climate of (low and irregular rainfall) is. The most important step in the construction of water storage tanks to choose the best point for the construction of the reservoir basin in order to reduce costs and increase efficiency. Chndmyarh different methods to decide the best option for finding a few options from there. Among these methods can be Tapsys two methods (TOPSIS) and hierarchical analysis (AHP) pointed... 

Dissipative particle dynamics (DPD) is an emerging mesoscopic computational method in which the interparticle forces arise because of coarse-graining at the molecular level. In the asymptotic limit of large length scales, the governing equations of continuum are reproduced, as demonstrated in this work. This method of simulation has the capability of simulating larger order of time and space in compare with dynamic molecular method. One of the important applications of DPD is simulating the dilute polymer solution. In this project, we developed a general code to simulate dilute polymer behavior which consists of polymeric forces and different types of usual DPD boundary conditions. This code... 

We study the Navier-Stokes equations with an extra Eddy viscosity term in the whole space . We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove that when the regularizing parameter goes to zero, the solution of the regularized system converges to a turbulent solution of the initial system. In the first chapter, we have dedicated the necessary preliminaries and then in the second chapter, we have introduced the types of solutions. The third chapter introduces the necessary tools and their properties, with the help of which in the next chapter we have been able to make estimates and obtain their extensions to prove... 

Streaming has some applications in medical and industrial science. This phenomena can increase or decrease efficiency of an acoustic system. Deliberate streaming used to eliminate heat exchanger is an example of desired applications. In the most cases, secondary flow is an undesired issue. Streaming in thermal buffer tube (TBT) of thermoacoustic stirling heat engine (TASHE) has some unwanted effects. The main goal of author is to simulate numerically periodic field in TBT with axisymmetric geometry and study the effects of variating geometry and turbulence on the intensity of streaming. According to inaccessible boundary conditions in TBT of TASHE, firstly, the field is numerically solved... 

The research on the automotive brake composite materials is very extensive due to its complex formulation and the used of diverse variety of materials. While various research activities has been applied in this research group, but there are many unknown areas. This subject with the arrival of new materials, especially nanometer materials, has received increasing attention. In this study, the effect of alumina nanoparticles on the performance of automotive brake friction materials were examined. Generally, alumina (as micro particles) used as the abrasive material for many years in the formulation of composite brake pads. But, the effect of alumina on the nanometer scale hasn't been examined... 

A 2D simulation has been carried out to study the effect of magnetic field on heat transfer and pressure drop of nanofluid flowing through a pipe filled with porous medium. The nanofluid flow is modeled as a single-phase flow, and Darcy–Brinkman–Forchheimer equation is employed to model fluid flow in porous media. A constant uniform heat flux was imposed on the walls of the cylinder, and the values of Darcy number, Hartmann number, and volume fraction of the nanoparticles were selected as 0.1, 200, and 0.2, respectively. Effects of parameters such as Reynolds number, the material of the porous medium (conductivity and porosity), and material of nanofluids have been investigated in the...