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diffusion-equation
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Reaction-diffusion equations with polynomial drifts driven by fractional brownian motions
, Article Stochastic Analysis and Applications ; Volume 28, Issue 6 , Oct , 2010 , Pages 1020-1039 ; 07362994 (ISSN) ; Sharif University of Technology
2010
Abstract
A reaction-diffusion equation on [0, 1]d with the heat conductivity k > 0, a polynomial drift term and an additive noise, fractional in time with H > 1/2, and colored in space, is considered. We have shown the existence, uniqueness and uniform boundedness of solution with respect to k Also we show that if k tends to infinity, then the corresponding solutions of the equation converge to a process satisfying a stochastic ordinary differential equation
Optimization of the direct discrete method using the solution of the adjoint equation and its application in the multi-group neutron diffusion equation
, Article AIP Conference Proceedings ; Volume 1389 , 2011 , Pages 1777-1781 ; 0094243X (ISSN) ; 9780735409569 (ISBN) ; Vosoughi, N ; Sharif University of Technology
2011
Abstract
Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning
Global existence, blow-up and asymptotic behavior of solutions for a class of p(x)-Choquard diffusion equations in RN
, Article Journal of Mathematical Analysis and Applications ; Volume 506, Issue 2 , 2022 ; 0022247X (ISSN) ; Hamdani, M. K ; Bayrami Aminlouee, M ; Sharif University of Technology
Academic Press Inc
2022
Abstract
In this paper, we investigate the local and global existence, asymptotic behavior, and blow-up of solutions to the Cauchy problem for Choquard-type equations involving the p(x)-Laplacian operator. As a particular case, we study the following initial value problem [Formula presented] where p,q,V:RN→R and α:RN×RN→R are continuous functions that satisfy some conditions which will be stated later on, and u0:RN→R is the initial function. Under some appropriate conditions, we prove the local and global existence of solutions for the above Cauchy problem by employing the abstract Galerkin approximation. Moreover, the blow-up of solutions and large-time behavior are also investigated. © 2021...
Selection and simulation of a proper microfluidic for hepatocyte culture
, Article 2015 22nd Iranian Conference on Biomedical Engineering, ICBME 2015, 25 November 2015 through 28 November 2015 ; 2015 , Pages 65-69 ; 9781467393515 (ISBN) ; Firoozabadi, B ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
The advent of microfluidics as suitable environments for culturing cells is associated with some challenges as shear stresses applied on the cells. Moreover, among all factors needed for cell viability, feeding hepatocytes with adequate oxygen is of great importance due to their high demand for oxygen compared the other cell types. In this paper three kinds of geometries has been studied in order that shear stresses would be in allowed range and provision of hepatocytes with sufficient oxygen concentrations has been ensured as well. In addition to supplying hepatocytes with oxygen, the range of its concentration has been adjusted in physiologic value so that it would be practical for further...
A macroscopic traffic flow model that includes driver sensitivity to the number of free spaces ahead
, Article Transportmetrica B ; 2017 , Pages 1-17 ; 21680566 (ISSN) ; Nassiri, H ; Sharif University of Technology
Abstract
This paper addresses the first-order extension of the Lighthill–Whitham– Richards (LWR) macroscopic traffic flow model. Although previous studies have focused on the fluid aspect of traffic flow, none have addressed the sensitivity of drivers to the number of free spaces within a certain distance ahead of the subject driver. To incorporate driver behavior, we used the number of free spaces ahead of subject drivers and their sensitivity to the number of free spaces within a certain distance ahead. The resulting model is a convection-diffusion model. By computing Einstein's diffusion equation and comparing it with the diffusion coefficient in the extended model, a theoretical relation for the...
A macroscopic traffic flow model that includes driver sensitivity to the number of free spaces ahead
, Article Transportmetrica B ; Volume 8, Issue 1 , 2020 , Pages 290-306 ; Nassiri, H ; Sharif University of Technology
Taylor and Francis Ltd
2020
Abstract
This paper addresses the first-order extension of the Lighthill–Whitham– Richards (LWR) macroscopic traffic flow model. Although previous studies have focused on the fluid aspect of traffic flow, none have addressed the sensitivity of drivers to the number of free spaces within a certain distance ahead of the subject driver. To incorporate driver behavior, we used the number of free spaces ahead of subject drivers and their sensitivity to the number of free spaces within a certain distance ahead. The resulting model is a convection-diffusion model. By computing Einstein's diffusion equation and comparing it with the diffusion coefficient in the extended model, a theoretical relation for the...
Higher order power reactor noise analysis: the multigroup diffusion model
, Article Annals of Nuclear Energy ; Volume 111 , 2018 , Pages 354-370 ; 03064549 (ISSN) ; Hosseini, A ; Vosoughi, N ; Sharif University of Technology
Elsevier Ltd
2018
Abstract
Power reactor noise analysis is one of the most powerful tools in online monitoring and diagnostics of nuclear power reactors. Unfortunately, since such an analysis belongs to the non-linear “parametric excitation” realm, its theoretical aspects and relations have been mostly carried out after linearization. In this paper a general framework, i.e. the Ladder Expansion Method, is developed to convert such equations to a series of coupled linear equations, up to any desired accuracy. This method is then applied to the single mode random fluctuations of the absorption cross sections in a power reactor which is modelled by the multigroup diffusion equation with multiple delayed neutron groups. A...
2D parallel and stable group explicit finite difference method for solution of diffusion equation
, Article Applied Mathematics and Computation ; Volume 188, Issue 2 , 2007 , Pages 1184-1192 ; 00963003 (ISSN) ; Davami, P ; Sharif University of Technology
2007
Abstract
Recently various versions of alternating group explicit or alternating group explicit-implicit methods were proposed for solution of diffusion equation. The main benefits of these methods are: good stability, accuracy and parallelizing. But these methods were developed for 1D case and stability and accuracy were investigated for 1D case too. In the present study we extend the new group explicit method [R. Tavakoli, P. Davami, New stable group explicit finite difference method for solution of diffusion equation, Appl. Math. Comput. 181 (2006) 1379-1386] to 2D with operator splitting method. The implementation of method is discussed in details. Our numerical experiment shows that such 2D...
A modified space - Time finite element method for simulation of immiscible incompressible two-phase flow in heterogeneous porous media
, Article International Journal for Numerical Methods in Fluids ; Volume 53, Issue 8 , 2007 , Pages 1221-1242 ; 02712091 (ISSN) ; Taghizadeh Manzari, M ; Sharif University of Technology
2007
Abstract
In this paper, a modified space-time method is presented for the simulation of convection-diffusion equations. The new method differs from the original space-time method in the sense that the weight functions for space and time are different. The performance of the proposed algorithm is studied for numerical simulation of incompressible immiscible two-phase flow in porous media. The governing equations consist of one conservation of mass equation for each phase, the Darcy law and one capillary-saturation correlation for the flow. By defining a global pressure, the governing equations lead to a system of nonlinear equations in terms of this global pressure, the velocity components and the...
New stable group explicit finite difference method for solution of diffusion equation
, Article Applied Mathematics and Computation ; Volume 181, Issue 2 , 2006 , Pages 1379-1386 ; 00963003 (ISSN) ; Davami, P ; Sharif University of Technology
2006
Abstract
A new group explicit method for solution of diffusion equation is presented. This method is based on domain decomposition concept and using asymmetric Saul'yev schemes for internal nodes of each sub-domain and alternating group explicit method for sub-domain's interfacial nodes. This new method has several advantages such as: good parallelism, unconditional stability, fully explicit nature and better accuracy than original Saul'yev schemes. The details of implementation and proving stability are briefly discussed. Numerical experiments on stability and accuracy are also presented. © 2006 Elsevier Inc. All rights reserved
Reconstruction of neutron flux distribution by nodal synthesis method using online in-core neutron detector readings
, Article Progress in Nuclear Energy ; 2020 ; Ghofrani, M. B ; Sharif University of Technology
Elsevier Ltd
2020
Abstract
The safety and optimal performance of nuclear reactors require online monitoring in the core. The present paper describes a method that avoids the solution of the time-dependent neutron diffusion equation, and it uses online readings of the fixed in-core neutron detectors to reconstruct the three-dimensional (3D) neutron flux distribution. The essential idea of the nodal synthesis method is the separation of time and space-dependence of the neutron flux distribution. The time-dependent section of the flux distribution is determined by in-core neutron detector readings, and the space-dependent section is obtained from pre-computed harmonics of the neutron diffusion equation. In online...
Reconstruction of neutron flux distribution by nodal synthesis method using online in-core neutron detector readings
, Article Progress in Nuclear Energy ; Volume 131 , 2021 ; 01491970 (ISSN) ; Ghofrani, M. B ; Sharif University of Technology
Elsevier Ltd
2021
Abstract
The safety and optimal performance of nuclear reactors require online monitoring in the core. The present paper describes a method that avoids the solution of the time-dependent neutron diffusion equation, and it uses online readings of the fixed in-core neutron detectors to reconstruct the three-dimensional (3D) neutron flux distribution. The essential idea of the nodal synthesis method is the separation of time and space-dependence of the neutron flux distribution. The time-dependent section of the flux distribution is determined by in-core neutron detector readings, and the space-dependent section is obtained from pre-computed harmonics of the neutron diffusion equation. In online...
Investigation on Improving Direct Discrete Method and its Application in Adjoint Diffusion Equation Numerical Solvers
, M.Sc. Thesis Sharif University of Technology ; Vosoughi, Naser (Supervisor)
Abstract
Numerical analysis method improvement is a topic of interest among all engineering disciplines. Regarding the fact that our ability to predict the behavior of a physical system is often limited by our computational resources, the efficiency of the employed numerical method is an important factor in the degree of approximation used in modeling. One of the recent numerical methods is the Cell Method (CM), which is also known as the Direct Discrete Method (DDM). This method combines some features of a variety of methods, especially finite volume and finite element, and gains some insight from the graph theory used in network analysis. The result is a method in which the set of equations which...
Neutron Noise Calculation Using High order Nodal Expansion Method
, M.Sc. Thesis Sharif University of Technology ; Vosoughi, Naser (Supervisor)
Abstract
This study consists of two parts: steady state calculations and neutron noise calculations in the frequency domain for two rectangular and hexagonal geometries. In the steady state calculation, the neutron diffusion and its adjoint equations are approximated by two-dimensional coordinates in two-group energy and are solved using the average current nodal expansion method. Then, by considering the node size in the dimensions of a fuel assembly, different orders of flux expansion are investigated. For verification purposes, the calculations have been performed by power iteration method for two test problems of BIBLIS-2D and IAEA-2D. For rectangular geometry with increasing flux expansion order...
Well-posedness of Two Mathematical Models for Alzheimer's Disease
, M.Sc. Thesis Sharif University of Technology ; Hesaaraki, Mahmoud (Supervisor)
Abstract
In season 1, we introduce a mathematical model of the in vivo progression of Alzheimer’s disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of Aβ -amyloid plaques based on the concentrations of Aβ oligomers, PrPC proteins, and the Aβ-×-PrPC complex, which are hypothesized to be responsible for synaptic tox- icity. We prove the well posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of β-amyloid is constant and also when it is described by a power law. In seson 2, We consider the existence and uniqueness of solutions of an initial-boundary...
On an improved Direct Discrete Method and its application in two dimensional multi-group neutron diffusion equation
, Article Annals of Nuclear Energy ; Volume 44 , June , 2012 , Pages 1-7 ; 03064549 (ISSN) ; Vosoughi, N ; Ayyoubzadeh, S. M ; Sharif University of Technology
2012
Abstract
An improvement to the Direct Discrete Method (DDM), also known as the Cell Method, has been discussed. The improvement is based on a duality theorem between the primal and dual complexes. Also, the analog counterpart of the Integral operator has been derived in this paper. The multi-group neutron diffusion is then derived, directly in a discrete algebraic form, according to this procedure. A numerical example has shown that this method would yield a high order of convergence (approximately 4.6) if its parameters are adjusted suitably. Finally, the method is applied to the 2D IAEA benchmark problem, and has shown to yield accurate solutions with a reasonably low number of unknowns
Solution of diffusion equation in deformable spheroids
, Article Annals of Nuclear Energy ; Volume 38, Issue 5 , 2011 , Pages 982-988 ; 03064549 (ISSN) ; Safari, M. J ; Vosoughi, N ; Sharif University of Technology
2011
Abstract
The time-dependent diffusion of neutrons in a spheroid as a function of the focal distance has been studied. The solution is based on an orthogonal basis and an extrapolation distanced related boundary condition for the spheroidal geometry. It has been shown that spheres and disks are two limiting cases for the spheroids, for which there is a smooth transition for the systems properties between these two limits. Furthermore, it is demonstrated that a slight deformation from a sphere does not affect the fundamental mode properties, to the first order. The calculations for both multiplying and non-multiplying media have been undertaken, showing good agreement with direct Monte Carlo...
The effect of the physical properties of the substrate on the kinetics of cell adhesion and crawling studied by an axisymmetric diffusion-energy balance coupled model
, Article Soft Matter ; Volume 11, Issue 18 , Mar , 2015 , Pages 3693-3705 ; 1744683X (ISSN) ; Shodja, H. M ; Malekmotiei, L ; Sharif University of Technology
Royal Society of Chemistry
2015
Abstract
In this paper an analytical approach to study the effect of the substrate physical properties on the kinetics of adhesion and motility behavior of cells is presented. Cell adhesion is mediated by the binding of cell wall receptors and substrate's complementary ligands, and tight adhesion is accomplished by the recruitment of the cell wall binders to the adhesion zone. The binders' movement is modeled as their axisymmetric diffusion in the fluid-like cell membrane. In order to preserve the thermodynamic consistency, the energy balance for the cell-substrate interaction is imposed on the diffusion equation. Solving the axisymmetric diffusion-energy balance coupled equations, it turns out that...
Robust control for time-fractional diffusion processes: Application in temperature control of an alpha silicon carbide cutting tool
, Article IET Control Theory and Applications ; Volume 12, Issue 15 , 2018 , Pages 2022-2030 ; 17518644 (ISSN) ; Tavazoei, M. S ; Sharif University of Technology
Institution of Engineering and Technology
2018
Abstract
Different real-world processes can be described by a linear model parameterised with respect to the processoperating point, as an uncertain parameter. The family of transport processes with long memory is a kind of these processeswhich are characterised by the parameterised time-fractional diffusion equations. This study proposes a generalised isodamping feature for achieving the phase margin invariance regardless of the uncertain parameter variations in control of timefractional diffusion processes. Also, the study suggests an analytical method to tune stabilising fractional-order proportional-integral/proportional-derivative controllers for adjusting a desired value for the phase margin at...
Neutron noise simulator based on the boundary element method (BEM)
, Article Annals of Nuclear Energy ; Volume 159 , 2021 ; 03064549 (ISSN) ; Mohamadbeygi, S ; Sharif University of Technology
Elsevier Ltd
2021
Abstract
The purpose of the present study is to develop the neutron diffusion solver and neutron noise simulator based on the Boundary Element Method (BEM). The 2-D, 2-G neutron/adjoint diffusion equation and corresponding neutron/adjoint noise equation were solved using the mentioned method. The developed neutron static and noise simulator based on the finite element method gives accurate results when the more number of the elements is used. The motivation of the present research is to use the boundary element method to reduce the computational cost. The boundary element method attempts to use the given boundary conditions to fit boundary values into the integral equation, rather than values...