Sharif Digital Repository

A Polygonal finite element method without conforming mesh was introduced by the authors for modeling large deformation elastoplastic problems. In this method, the geometry and interfaces of the problem are modeled on a uniform mesh. The boundaries are defined on the uniform background mesh using the level set method. Different polygonal elements will be created at the intersection of the interface and the uniform mesh. Polygonal element shape functions are used for the interpolation. In this paper, the capability of this polygonal finite element approach for modeling large deformational frictionless dynamic contact-impact problems is investigated. Contact interfaces are modeled independent... 

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, . . .This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution  

In the most cosmological models which already have putted forth, metric has a spherical symmetry; however, according to the galaxy’s shape is not a real approximation. In order to build a more acqurate model, by applying a particular conformal transformation on the static vacuum solution, we introduce a new metric which is axially symmetric and also it approaches to FLRW metric at space infinity. The cosmological model according to this metric has especial features;The solution we have found represent a spacetime which is axially symmetric although it leads to a spherically symmetric Einstein tensor. Therefore, we have found a solution of Einstein equations representing a spherically... 

We extend the non-relativistic AdS/CFT correspondence to the fermionic fields. In particular we study the two point function of a fermionic perator in non-relativistic CFTs by making use of a massive fermion propagating in geometries with Schrodinger group isometry. Although the boundary of the geometries with Schrodinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established، using the general procedure of AdS/CFT correspondence، we see that the resultant two point function has the expected form for fermionic operators in non-relativistic CFTs، though a non-trivial regularization may be needed. Also we study Weyl symmetry for non-relativistic... 

Many statistical systems such as earthquakes, road trafcs, forest fres, neurocortical avalanches etc. exhibit self-organized criticality (SOC). In such systems without tuning extrenal parameters, the system arrives at criticality. During recent decades, a number of models are introduced which show the same charactristics. These models have made a platform to investigate the physics of self-organized criticality. Among them, sandpile models are the best known models. They exhibit critical behaviour such as scaling laws. Also in some of them conformal invariance is checked nummerically.Most of sandpile models deal with slope parameters, that is, the main dynamical parameters are the local... 

NMR spectroscopy as a powerful technique is often used to investigate on structural and conformational studies on proteins and drug compounds. In this work, conformations and structural properties of drug compounds and some nucleoside derivations have been studied using advanced NMR techniques including H-H COSY, HMQC, HMBC and NOESY and quantum based calculations.Experimental analysis on Valsartan show that there are two simultaneous conformers (M and m) with unequal population in M-m type solvents and two stable conformers (N and n) in the N-n type solvents. As the results show, different intramolecular hydrogen bond is the reason for stability af all available conformers. In the... 

Conformal Field Theory provides an efficient method for studying physical problems in critical point. Correlation length becomes converge in this point. It can also be clarified that some curves are observed in geometrical phase transition which are conformal invariant and they can be studied using SLE(k). The first mathematical generalization of SLE(k) while keeping the self-similarity property, leads to SLE(k,p). Conformal field theory and SLE are interrelated and their parameters are interpretable for each other. One usually studies the problem in the upper-half plane. Here we consider the problem using a map like (w=L/π Ln z) between the upper-half plane and a special region (e.g. a... 

The theory of self-organized criticality is originally introduced by Bak, Tang and Wiesenfeld as a general mechanism that can explain the behaviour of complex systems which naturally organize themselves into a critical state. They defined the sandpile model as an example of slowly driven and dissipative complex system to explain the concept of self-organized criticality. From the definition of the model, extensive work has been done on this model. Thanks to the Abelian property of the model, many statistical results have been derived exactly. Other properties of the model such as critical exponents and dynamical behaviors have been also studied using the mapping with some statistical models... 

Schramm – Loewner Evolution (SLE) is a framework which helps to classify interfaces in critical models. At criticality two or more phases of the model are separated by an interface. In two dimensions this interface is a simple random curve, which can be addressed by SLE theory. This classification has crucial rule in our understanding of statistical models. In spite of our understanding of2 dimensional statistical models and 1+1dimensional quantum field theories, little workhas been done on these models out of criticality. In this thesis we focus on the Schramm-Loewner Evolutions and conformal field theoriesin vicinity of critical points. To this end we state the theories which the... 

At first the killing vector fields will be investigated. Conditions are introduced for the hypersurface of a Riemannian manifold with a killing vector field to be equipped with the same killing vector field. Then 2-killing vector field is studied and its relation with killing vector fields and monotone vector fields is presented. After that conformal vector fields are discussed and conditions are introduced in order that the Riemannian manifold equipped with a conformal vector field, isisometric to n-dimensional sphere with constant curvature. Finally we will present the conditions which conformal vector field is a 2-killing vector field. Then we will present the results in which the... 

In this thesis an analytical solution is introduced for finding the elastic fields of stress and strain in a confocal elliptic ring at the state of general plane problem. A confocal elliptic ring is a doubly connected region which its external and internal boundaries are ellipses with the same focal points. We used the method of complex variables, the functions of Kolosov-Muskhelishvili potentials, Laurent series expansion for analytical functions, the method of the analytic continuation of Milne-Thomson, elliptic hyperbolic coordinates, and two dimensional conformal mapping to do this study. the importance of this analysis is because we can simulate some problems of the elasticity by... 

In this thesis, we show that conformal Chern–Simons gravity in three dimensions has various holographic descriptions. They depend on the boundary conditions on the conformal equivalence class and the Weyl factor. The boundary conditions on the Weyl factor of the metric lead to three physically distinct scenarios: I. trivial Weyl factor, II. non-trivial but fixed Weyl factor and III. free Weyl factor. The metric is not necessarily asymptotically AdS in cases II and III, but nevertheless a dual CFT appears to emerge. We focus on a particular case III where an affine U(1) algebra related to holomorphic Weyl rescalings shifts one of the central charges by 1. The Weyl factor then behaves as a... 

In this thesis, with using the holographic renormalization we study couple of recently discovered gravitational theories, New Massive Gravity and Critical Gravity. We show that the dual field theory to each of them, is logarithmic conformal field theory. Also we study the Topologically Massive Gravity at critical point with hamiltonian holographic renormalization which is completely different from another approachs that are used to analys this theory. We show that albeit the dual field theory to this gravitational theory is logarithmic conformal field theory, but we can define completely consistent Wald’s charges, holographic charges and Noether’s charges for it  

According to the reported field experiences, excess water production from high permeable thief zones of oil reservoirs is the main source of severe operational problems and economic issues. Application of Preformed Particle Gels (PPGs) is an effective technique to overcome this problem. Static test analysis is a primary method for evaluating the performance of PPGs material at different conditions of pH, salinity, etc. However, the effect of the presence of oil and rock on the kinetics of swelling/de-swelling of PPGs is not well understood. Also, considering the vast field application of Co_2-based oil recovery methods, it is interesting to study the effect of carbon dioxide gas on swelling... 

Discretely holomorphic observables have recently been proposed for two dimensional lattice models at criticality, whose correlation functions satisfy a discrete version of Cauchy-Riemann relations. Existence of these observables appears to have a deep relation with integrability of the model. On the other hand at critical points of these models, there exist entities known as discrete parafermions whose Boltzmann weights satisfy the Yang-Baxter Equations. For this reason, finding parafermionic observables in any lattice model is equivalent to proof of solvability. This thesis is a step towards understanding the relation between Parafermions and Solvability. For instance, the Boltzmann weights... 

Routers play a key role in transferring information between various Networks. It is very important to make sure about the compatibility of OSPF in a router with its standard description. In this regard, before presenting or applying a router and also evaluating its performance, it is necessary to carry out conformance test with the help of network equipment testers Tester designers extract test cases from protocol standard description through non-formal ways and exam them on network equipment.
In this thesis, a part of OSFP protocol has been modeled through colored Petri nets. In this regard, two sections of OSPF RFC have been model checked: neighbor state machine and data base... 

Percolation is a simple probabilistic model which exhibits a phase transition. Here, we study this critical model from properties of random curves which in the scaling limit, appear as features seen on the macroscopic scale, in situations where the microscopic scale is taken to zero. Among the principal questions are the construction of the scaling limit, and the discription of some of the emergent properties, in particular the behavior under conformal maps Over the past few years, SLE has been developed as a valuable new tool to study the random paths of the scaling limit of two-dimensional critical models, and it is believed that SLE is the conformally invariant scaling limit of these... 

Classical quench is the act of sudden change in the temperature of a system. This process is not new and has been used in some branches of science, like the smithing industry to produce a hard and stiff metal objects. Quantum Quench is the deformation of system's Hamiltonian in short time interval. This quantum version of quench is around for a few years and has attracted a lot of attention after its experimental realization in Ultracold Atoms setup. Suppose we have hamiltonian which depends on the constant g_0 which is the dynamical parameter of the system. It could be interaction strength between elements in the system or the external electric field amplitude on the system. At an arbitrary... 

We study different aspects of non-relativistic conformal symmetries. Schrodinger and Galilean Conformal Algebra (GCA) are reviewed extensively. We as well study possible extensions of non-relativistic conformal symmetries. We find a new class of infinite dimensional non-relativistic conformal symmetries in 2+1. We study logarithmic representation of Schrodinger symmetry. As well we utilize contraction approach and obtain both ordinary and logarithmic representations of GCA. Finally we investigate some aspects of logarithmic GCA in the context of holography principle  

In this Thesis we study the string theory discription of non-relativistic quantum ?eld theories.In other statement we study the duality between gravity and gauge theory with non-relativistic symmetry.We discuss that this duality works in non rel- ativistic sense.We study two kind of non-relativistic theories that one of them camefrom string theory and other model obtained by special transformation of original relativistic theory and we see that how duality can be work for these models.Also dual picture of semi-classical string in the background that found from string theorystudied.We also study the motion of particle in a hot plasma and we ?nd a sign of non-relativisic duality really works