Sharif Digital Repository

We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two-dimensional magnetohydrodynamics is discussed  

Correlation functions of logarithmic conformal field theory is investigated using the ADS/CFT correspondence and a novel method based on nilpotent weights and 'superfields'. Adding an specific form of interaction, we introduce a perturbative method to calculate the correlation functions. © 2004 Elsevier B.V. All rights reserved  

Logarithmic conformal field theory is investigated using the ADS/CFT correspondence and a novel method based on nilpotent weights. Using this device we add ghost fermions and point to a BRST invariance of the theory. © 2001 Elsevier Science B.V. All rights reserved  

We study logarithmic conformal field theories (LCFTs) through the introduction of nilpotent conformal weights. Using this device, we derive the properties of LCFTs such as the transformation laws, singular vectors and the structure of correlation functions. We discuss the emergence of an extra energy momentum tensor, which is the logarithmic partner of the energy momentum tensor. © 2001 Elsevier Science B.V  

We propose a general framework for deriving the OPEs within a logarithmic conformal field theory (LCFT). This naturally leads to the emergence of a logarithmetic partner of the energy momentum tensor within an LCFTand implies that the current algebra associated with an LCFT is expanded. We derive this algebra for a generic LCFTand discuss some of its implications. We observe that two constants arise in the OPE of the energy-momentum tensor with itself. One of these is the usual central charge  

We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions  

In the present paper we investigate the problem of water propagation in 2 dimensional (2D) petroleum reservoir in which each site has the probability p of being occupied. We first analyze this propagation pattern described by Darcy equations by focusing on its geometrical features. We find that the domain-walls of this model at p=pc ≃ 0.59 are Schramm-Loewner evolution (SLE) curves with κ=3.05 ∓ 0.1 consistent with the Ising universality class. We also numerically show that the fractal dimension of these domain-walls at p=pc is Df ≃ 1.38 consistent with SLEκ=3. Along with this analysis, we introduce a self-organized critical (SOC) model in which the water movement is modeled by a chain of... 

In this paper, we consider several known growth processes with height-dependent noise. This type of noise is interesting from a theoretical standpoint, for example, it paves the way to the derivation of the exact height distribution of the KPZ equation through the Hopf–Cole transformation. In addition, it may have implications for experimental growth processes. Using numerical methods, we observe that adding such a noise to different growth processes, can change their universality class or ruin the scaling laws. In the case of Mullins–Herring equation, a two-fold cross-over is observed. © 2020 Elsevier B.V  

We consider the Coulomb gas model on the upper half-plane with different boundary conditions, namely, Dirichlet, Neumann and mixed. We relate this model to SLE(κ, ρ) theories. We derive a set of conditions connecting the total charge of the Coulomb gas, the boundary charges, the parameters κ and ρ. Also we study a free fermion theory in presence of a boundary and show with the same methods that it would lead to logarithmic boundary changing operators. © Elsevier B.V. All rights reserved  

In this paper we derive the scaling fields in c = -2 conformal field theory associated with weakly allowed clusters in Abelian sandpile model and show a direct relation between the two models. © 2005 Elsevier B.V. All rights reserved  

Formal Loewner evolution is connected to conformal field theory. In this Letter we introduce an extension of Loewner evolution, which consists of two coupled equations and connect the martingales of these equations to the null vectors of logarithmic conformal field theory. © 2004 Elsevier B.V. All rights reserved  

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Our simulation results show that the (Abelian) BTW sandpile model, the (non-Abelian) Zhang model, and the ("Abelian") Manna model possesses different "weak chaos" exponents, so they may belong to different universality classes. Finally, we show that getting off the critical point destroys this behavior in these models  

In this paper we investigate the effect of the number of dissipative sites in an Abelian sandpile model. The dissipative sites are considered to be in the bulk rather than in the boundary. In such systems, statistics of avalanches smaller than a certain size obey a power law. We have seen that the exponents associated with these power law behaviors change slightly as the number of dissipative sites is decreased. We have found that the zero dissipation limits of these exponents are independent of size. Therefore we suggest that the previously-seen dependence of the exponent on the system size is because of the number of dissipative sites rather than the system size. Also it is observed that... 

In this paper we consider the Bak, Tang, and Wiesenfeld (BTW) sand-pile model with local violation of conservation through annealed and quenched disorder. We have observed that the probability distribution functions of avalanches have two distinct exponents, one of which is associated with the usual BTW model and another one which we propose to belong to a new fixed point; that is, a crossover from the original BTW fixed point to a new fixed point is observed. Through field theoretic calculations, we show that such a perturbation is relevant and takes the system to a new fixed point  

In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used in quantum field theory (QFT) where the bare values of the parameters of the theory run when an interaction is added. In this paper, we review some of these techniques and introduce some new ones in line with QFT methods. Moreover, we investigate the case of more than one oscillator to see how the frequencies of small oscillations change when non-linear terms are added to a linear system and observe an interesting beat phenomenon in degenerate coupled... 

The Abelian sandpile model (ASM) is a paradigm of self-organized criticality (SOC) which is related to c ≤ -2 conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing, and consider them in the presence of a boundary. © 2007 IOP Publishing Ltd  

We study numerically the statistics of curves which form the boundaries of toppling wave clusters in the deterministic Bak, Tang and Wiesenfeld sandpile model and stochastic Manna model on a square lattice. We consider the Abelian version of each model. Multiple tests show that the boundary of toppling wave clusters in both deterministic and stochastic models can be described by SLE curves with diffusivity = 2  

We insert some asymmetries into the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the corresponding field theories. Also we find the fields associated with some height variables. © 2008 IOP Publishing Ltd