Growth models on the Bethe lattice

I report on an extensive numerical investigation of various discrete growth models describing equilibrium and nonequilibrium interfaces on a substrate of a finite Bethe lattice. An unusual logarithmic scaling behavior is observed for the nonequilibrium models describing the scaling structure of the infinite dimensional limit of the models in the Kardar-Parisi-Zhang (KPZ) class. This gives rise to the classification of different growing processes on the Bethe lattice in terms of logarithmic scaling exponents which depend on both the model and the coordination number of the underlying lattice. The equilibrium growth model also exhibits a logarithmic temporal scaling but with an ordinary power law scaling behavior with respect to the appropriately defined lattice size. The results may imply that no finite upper critical dimension exists for the KPZ equation.Comment: 5 pages, 5 figure

Properties of recoverable region and semi-global stabilization in recoverable region for linear systems subject to constraints

This paper investigates time-invariant linear systems subject to input and state constraints. It is shown that the recoverable region (which is the largest domain of attraction that is theoretically achievable) can be semiglobally stabilized by continuous nonlinear feedbacks while satisfying the constraints. Moreover, a reduction technique is presented which shows, when trying to compute the recoverable region, that we only need to compute the recoverable region for a system of lower dimension which generally leads to a considerable simplification in the computational effort

Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the probability for the initially flat geometry to be chosen and compute the phase diagram as a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal ensemble Tracy-Widom (TW) distribution for p0.5. For p=0.5 where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in nonequilibrium transport and traffic flow.Comment: 5 pages, 6 figures, Phys. Rev. Lett. (2019) (accepted

Apical Debris Extrusion with Conventional Rotary and Reciprocating Instruments

Introduction: The aim of the present study was to compare the amount of apical debris extrusion after preparation using hand files, reciprocating files, and full rotary nickel-titanium systems. Methods and Materials: One hundred extracted human mandibular molars with two separated canals in mesial root were divided into five groups and prepared using reciprocating systems (Reciproc and Safesider endodontic reamer files), full rotary systems (Mtwo and Neoniti A1 files) and hand instrumentation systems. Endodontic access was prepared and a #15 K-file was passed beyond the apex of the mesiobuccal canal by 1 mm to ensure the canal patency. All mesiobuccal canals were prepared 1 mm shorter than the anatomic apex. In each case, extruded debris was collected in an Eppendorf tube and weighed after desiccation. The mean weight of extruded material was calculated in each group. The analysis was carried out using the Kruskal–Wallis test followed by two tailed and Mann-Whitney U test at a significance level of 0.05. The Bonferroni correction was also applied to correct multiple comparisons. Results: There was a statistically significant difference between the reciprocal and other techniques in debris extrusion (P<0.05). The order of groups ranked in terms of debris extrusion from the lowest to highest was as follows: 1) Hand instrumentation group (with crown down technique), 2) Mtwo group, 3) Neoniti A1 group, 4) Safesider endodontic reamer group, and 5) Reciproc group. Conclusion: Based on this in vitro study, all systems have some apical debris extrusion; however, using the hand instrumentation system resulted in extrusion of significantly less debris compared to the Reciproc group. It seems that hand and rotary instrumentation systems are better than reciprocating instrumentation systems in terms of the amount of debris extrusion.Keywords: Endodontics; Root Canal Preparation; Rotary Instrumentatio

Internal stabilization and external LpL_p stabilization of linear systems subject to constraints

Having studied during the last decade several aspects of several control design problems for linear systems subject to magnitude and rate constraints on control variables, during the last two years the research has broadened to include magnitude constraints on control variables as well as state variables. Recent work by Han et al. (2000), Hou et al. (1998) and Saberi et al. (2002) considered linear systems in a general framework for constraints including both input magnitude constraints as well as state magnitude constraints. In particular, Saberi et al. consider internal stabilization while Han et al. consider output regulation in different frameworks, namely a global, semiglobal, and regional framework. These problems require very strong solvability conditions. Therefore, a main focus for future research should focus on finding a controller with a large domain of attraction and some good rejection properties for disturbances restricted to some bounded se

Difference between the Actual and Labeled Concentrations of Several Domestic Brands of Sodium Hypochlorite

Introduction: Sodium hypochlorite (NaOCl) is extensively used in root canal treatment and its efficacy depends on the concentration of free available chlorine (FAC). This study aimed to assess the chlorine content of 10 domestically manufactured household bleach products available in the Iranian market and evaluate the effect of temperature, time and daily bottle uncapping on FAC concentration and pH of these products. Methods and Materials: One-liter bottles of 10 available brands of household bleach (n=4 of each brand) were collected and randomly divided into four groups (n=10). Two groups were refrigerated at 4°C while the remaining two were stored at room temperature. One group of refrigerated and one group of room temperature samples were subjected to daily bottle uncapping followed by agitation and recapping for 3 months (six times a week to simulate weekly office work). The remaining bottles remained untouched and served as controls. The concentration of FAC in each sample was measured using the iodometric titration assay, and the pH was measured using a calibrated pH-meter at baseline and 1, 2 and 3 months. The results were analyzed using the one-way ANOVA and t-test. Results: The mean concentration of FAC in the solutions was 4.87±0.19% at baseline. The measured concentration of sodium hypochlorite was different from the labeled value. The concentration of FAC decreased over time in all samples; the greatest reduction occurred in room temperature samples subjected to daily uncapping while the smallest reduction occurred in refrigerated, capped bottles (19% and 1.9%, respectively). The pH of all products decreased over time. The mean reduction in pH was 1.1 for the samples stored at room temperature for 3 months and 0.8 for the refrigerated samples. Conclusion: This in vitro study showed that the expected concentration of sodium hypochlorite solution made of household bleach for endodontic purposes is different from its actual concentration.Keywords: Chlorine Compounds; Hydrogen-ion Concentration; Root Canal; Sodium Hypochlorite