Sharif Digital Repository

Best way to extinguish one kind of species is targeting their habitat instead targeting the species directly. Targeting tumor microenvironment is source of several methods of cancer immunotherapy attending to the effective factor at microenvironment appears as main spot in designing immunotherapy protocols. Cells compete in an atmosphere in which they create different mechanisms in tumor microinvronment. Now, we can make abstract models of these cellular mechanism using accurate mathematical instruments, this is theoretical biology which is as subset in the field of mathematical biology. In these models, we can identify parameters that has more therapeutic value in the microenvironment.... 

We study synaptically coupled neuronal networks to identify the role of coupling delays in network synchronized behavior. Identifying the effect of delay is important for understanding information processing functions in the brain and Many studies have been done on the effects of delays on networks where the synapses are exclusively excitatory or inhibitory, but few address networks with both. Thus we focus on this case. In this thesis, we consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory are coupled with time-delayed synapses. Using singular perturbation analysis, we will study the dynamic behavior of the network... 

In this thesis, we propose a first-order interior-point method for linearly constrained smooth optimization which was recently proposed in the literatuare that unifies and extends first-order affine-scaling method and replicator dynamics method for standard quadratic programming. Global convergence and, in the case of quadratic program, the (sub)linear convergence rate and iterate convergence results are derived.The method is implemented and numerical experiments on simplex onstrained problems with 1000 variables is reported  

In this thesis, unconstrained convex quadratic optimization problems subject to parameter perturbations are considered. A robustification approach is proposed and analyzed which reduces the sensitivity of the optimal function value with respect to the parameter. Since reducing the sensitivity and maintaining a small objective value are competing goals, strategies for balancing these two objectives are discussed. Numerical examples illustrate the approach  

Nowadays, due to the increasing importance and penetration of microgrids, solving the microgrid optimal sizing problem has become more important. The current utility grid and conventional energy sources are mainly ac, however, increasing rate of the replacement of the ac load with dc load lead to a more efficient dc system. So choosing the optimal type of microgrid as a way to increase efficiency of these systems would be a serious issue. This thesis establishes a planning model which finds the optimal size and type of a microgrid to minimize total cost. Total cost includes investment, operation and reliability cost of the microgrid. Sizes of DGs, converters and transformer linking the... 

Singular differential equations have a wide range of applications. Hardy singularities, which are connected to inequalities of the same name and have various extensions, are the most well-known singularities. The application of Hardy inequalities in quantum physics and also in the linearization of reaction-diffusion equations in thermodynamics and combustion theory motivates researchers to examine them. Singularities on a domain's boundary are another well-known type of singularity. In the study of fluid mechanics and pseudoplastic flows, these singularities emerge.Differential equations with coefficients or functions that are simply functions belonging to $ L^1 $, or bounded Radon measures,... 

Carbo nanocones are one of the nanostructures that are investigated and takes a large deal of attention in nanotechnology. In the present study the governing equilibrium equations of motion of carbon nanotubes under external pressure are derived using a nonlocal shell model and first order shear deformation theory. The natural frequency and buckling load are extracted using modal method along with Galerkin technique.Afterthis using both Winkler and Pasternak elastic foundation models, the governing equations of motion of nanocones embedded in the elastic medium extracted using a novel approach with the nonlocal shell model along with Hamilton’s principle. These equations solved using... 

Renewable energy resources, e.g. wind, solar and geothermal, experience rapid progresses in electric power industry all over the world. So, it becomes essential that these free-emission electrical energy resources be integrated in the existing generating capacity planning procedures. On the other hand, the uncertain and intermittent nature of these energies has led to some problems in their integration in power systems. The reserve requirement in a renewable-based power system is a main challenge, which has to be addressed properly. In this way, this research presents an analytical approach, based on the modified PJM method, to quantify the risk of renewable energies commitment during the... 

In recent decades, the study of Nano and Micro Electromechanical Systems (NEMS and MEMS) as in micro sensors and actuators or in Atomic Force Microscopes (AFM) attracted considerable attention. Since an indispensable part of such systems is a nano or micro flexible beam, the inevitable undesirable vibrations of the flexible beam necessitate the implementation of vibration control strategies. Recently, some cutting edge experiments on statics and dynamics behavior of micro beams have been conducted that reveal some deviations from the prediction of classical theories, and hence this leads to development of strain gradient elasticity theory. In addition, the often-adopted finite dimensional... 

Direct/inverse scattering of high frequency SH-waves by a circular micro-/nano-fiberembedded in an infinite elastic isotropic medium is addressed in the framework of couple stresstheory with micro inertia. The inadequacy of classical theory of elasticity in the problems dealingwith propagation of high frequency waves as well as the problems concerning the elastic fields inthe vicinity of micro-/nano-size defects in which the wavelengths and the size of the defects arecomparable to intrinsic length of the material is well-known. These dilemmas can be remedied byemploying the more accurate higher order continuum theories. So, in the context of couple stresstheory with micro inertia, the... 

In the thesis , we present a universal model of brain tissue microstructure that dynamically links osmosis and diffusion with geometrical parameters of brain extracellular space (ECS) . In the first part , we investigate the biological aspects of the model , and in the second , we analysis the model in the mathematical framework . The first part : Our model robustly describes and predicts the nonlinear time dependency of tortuosity ($\lambda = \sqrt{D/{D^{*}}}$) changes with very high precision in various media with uniform and nonuniform osmolarity distribution , as demonstrated by previously published experimental data ($D$ = free diffusion coefficient , $D^{*}$ = effective... 

In this thesis, we study diffusive heterogeneous predator-prey system with Holling type-II functional response in the presence of harvesting in prey equation i.e.8>>>>><>>>>>: Δu = u a(x)u2 buv1 + mu ch(x) inΩ;Δv = v v2 +duv1 + muinΩ;@u = @v = 0 on @Ω,where Ω is a smooth bounded region in RN and a(x) is a nonnegative continuous function on Ω, with Ω0 a region such that Ω0 Ω and a(x) > 0on ΩnΩ0. We show that in the case of weak prey growth rate, i.e. less than the first eigenvalue of Δ in Ω0 with Dirichlet boundary condition,the system has a positive solution for the values of in a bounded interval and c > 0 sufficiently small. We also investigate the multiplicity of positive solutions... 

The development of communication infrastructure in power systems has provided the grid with the availability of accurate information and has increased the reliability of the grid and its responsibility to disturbances. However, there have been some concerns about the negative impacts of the reliance on the information infrastructure. Inadequacies in the control and communication systems have been reported to be the contributing factors to situations that led to major blackouts. The functionality and reliability of the power grid is undoubtedly influenced by its communication infrastructure. In this thesis we are trying to model and analyze the failures that may occur in a power system and...