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kasbi-gharahasanlu--tohid
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Minimal Translation Surfaces in Sol_3 and Nil_3
, M.Sc. Thesis Sharif University of Technology ; Fanai, Hamid Reza (Supervisor)
Abstract
A surfaceMin the Euclidean space is called a translation surfaceif it is given by the graph z(s,t)=f(s)+g(t), where f and gare smooth functions on some interval of R. These surfaces are called translation surfaces since its parameterization X(s,t)=(s,t,f(s)+g(t) ) can be written as the sum of two curves (translation), namely , X(s,t)=(s,0,f(s) )+(0,t,g(t) )
In this work , Minimal surfaces in Sol_3 and Nil_3have been studied,where Sol_3and Nil_3are two model geometry of the eight geometries of Thurston. We propose a similar problem in Sol_3 and Nil_3 changing the additive + in the Euclidean space by the group operation * of Sol_3 and Nil_3, such that we have X(s,t)=α(s)*β(t), where α...
In this work , Minimal surfaces in Sol_3 and Nil_3have been studied,where Sol_3and Nil_3are two model geometry of the eight geometries of Thurston. We propose a similar problem in Sol_3 and Nil_3 changing the additive + in the Euclidean space by the group operation * of Sol_3 and Nil_3, such that we have X(s,t)=α(s)*β(t), where α...
Protein Aggregation in Biological Membrane
, M.Sc. Thesis Sharif University of Technology ; Jalali, Mir Abbas (Supervisor) ; Ejtehadi, Mohammad Reza (Co-Advisor)
Abstract
Aggregation of membrane proteins plays a determinative role in many biological processes، such as signal transduction, cell division and endocytosis. In the present study, we have investigated the interaction between proteins in vesicles by means of coarse-grained molecular dynamics simulations. In the first step, a number of periodic lipid bilayers were simulated and their physical properties were calculated. Then, bilayers were immersed in water and converted into spherical vesicles via a selforganizing process . Finally two proteins were embedded into the vesicle and the potential of mean force (PMF) respect to the angle between them was obtained using umbrella sampling. This process was...