Avalanche frontiers in dissipative abelian sandpile model as off-critical SLE(2)

Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with diffusivity parameter $\kappa = 2$. In this paper we consider the dissipative ASM and study the statistics of the avalanche and wave frontiers for various rates of dissipation. We examine the scaling behavior of a number of functions such as the correlation length, the exponent of distribution function of loop lengths and gyration radius defined for waves and avalanches. We find that they do scale with the rate of dissipation. Two significant length scales are observed. For length scales much smaller than the correlation length, these curves show properties close to the critical curves and the corresponding diffusivity parameter is nearly the same as the critical limit. We interpret this as the ultra violet (UV) limit where $\kappa = 2$ corresponding to $c=-2$. For length scales much larger than the correlation length we find that the avalanche frontiers tend to Self-Avoiding Walk, the corresponding driving function is proportional to the Brownian motion with the diffusion parameter $\kappa =8/3$ corresponding to a field theory with $c = 0$. This is the infra red (IR) limit. Correspondingly the central charge decreases from the IR to the UV point.Comment: 11 Pages, 6 Figure

Patterned and Disordered Continuous Abelian Sandpile Model

We study critical properties of the continuous Abelian sandpile model with anisotropies in toppling rules that produce ordered patterns on it. Also we consider the continuous directed sandpile model perturbed by a weak quenched randomness and study critical behavior of the model using perturbative conformal field theory and show the model has a new random fixed point.Comment: 11 Pages, 6 figure

Lamina Cribrosa and Choroid Features and Their Relationship to Stage of Pseudoexfoliation Glaucoma.

PurposeTo better understand the relationship of lamina cribrosa (LC) and choroid features to the severity of pseudoexfoliation glaucoma (PXG).MethodsIn this cross-sectional study, 137 eyes of 122 subjects (47 eyes with moderate/advanced PXG [mean deviation (MD), -15.0 ± 7.7 dB], 34 eyes with mild PXG [MD, -2.7 ± 1.5 dB], 32 aged-matched pseudoexfoliation syndrome [PXS] eyes, and 24 aged-matched control eyes) were investigated. Optic discs, LC thickness, and anterior LC depth (ALD; midsuperior, center, and midinferior) as well as peripapillary choroidal thickness were determined. Linear mixed modeling was used to adjust for age, sex, and axial length.ResultsA progressive decrease in LC thickness was found when comparing controls (271.9 ± 61.3 μm), PXS (212.6 ± 51.5 μm), mild PXG (180.8 ± 24.6 μm), and moderate/advance PXG (138.9 ± 37.5 μm) (P < 0.001). ALD was greater (P < 0.001) in moderate/advance glaucoma (306.7 ± 105.3 μm) and mild PXG (209.5 ± 79.7 μm) compared with PXS (155 ± 86.7 μm) and healthy controls (149.2 ± 103 μm). Although eyes with moderate/advance PXG had the thinnest choroid (117.2 ± 36.6 μm), choroidal thickness was comparable in mild PXG, PXS, and controls (150.0 ± 46.1, 159.7 ± 65.5, and 157.5 ± 51.1 μm, respectively; P = 0.002). Worse MD was the only factor associated with thinner LC (β = 2.344, P < 0.001) and choroid (β = 1.717, P = 0.009 μm) in PXG eyes. Higher IOP (β = 4.305, P = 0.013) and worse MD (β = -6.390, P < 0.001) were associated with deeper ALD in PXG.ConclusionsIn pseudoexfoliation, LC thinning is an early sign, and there is progressive thinning with advancing glaucoma. Choroidal thinning is observable only with moderate/advanced glaucoma. In PXG eyes, LC thickness, depth, and peripapillary choroidal thickness are associated with glaucoma severity

Jordan derivations on certain Banach algebras

In this paper, we study the types of Jordan derivations of a Banach algebra $A$ with a right identity $e$. We show that if $eA$ is commutative and semisimple, then every Jordan derivation of $A$ is a derivation. In this case, Jordan derivations map $A$ into the radical of $A$. We also prove that every Jordan triple left (right) derivation of $A$ is a Jordan left (right) derivation. Finally, we investigate the range of Jordan left derivations and establish that every Jordan left derivation of $A$ maps $A$ into $eA$

Spatial Asymmetric Two dimensional Continuous Abelian Sandpile Model

We insert some asymmetries in the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the field theory corresponding to the models. Also we find the fields associated with some height variables.Comment: 14 Pages, 11 Figure

Experimental Investigation on Supercavitating Flow over Parabolic Cavitators

In this paper experimental study was carried out to investigate supercavitation around parabolic cavitators. Various types of cavitators, such as disk, cone, and parabolic, were designed and manufactured. Also, the shape of the cavities formed behind these bodies were considered and compared. Dimensionless parameters such as dimensionless length and the diameter of the cavity as well as the dimensionless required air flow on the cavitators were obtained. The results showed that parabolic cavitators have an optimum design in comparison with the disk and cone cavitators due to their insignificant capability to reduce the drag force, yet the cavity’s length has a moderate size. It was also observed that this type of cavitator is capable of forming a cavity with a dimensionless length up to L/d= 33 and a dimensionless width up to D/d= 3.6. Moreover, parabolic cavitators require the highest amount of air injected in comparison with the cone and disk types; therefore, they operate in lower cavitation numbers. Since no other experimental data has been reported so far, this work reports the experimental characteristic behavior of parabolic cavitators