Self-similar but not conformally invariant traces obtained by modified Loewner forces

The two-dimensional Loewner exploration process is generalized to the case where the random force is self-similar with positively correlated increments. We model this random force by a fractional Brownian motion with Hurst exponent H≥1/2≡H_{BM}, where H_{BM} stands for the one-dimensional Brownian motion. By manipulating the deterministic force, we design a scale-invariant equation describing self-similar traces which lack conformal invariance. The model is investigated in terms of the "input diffusivity parameter" κ, which coincides with the one of the ordinary Schramm-Loewner evolution (SLE) at H=H_{BM}. In our numerical investigation, we focus on the scaling properties of the traces generated for κ=2,3, κ=4, and κ=6,8 as the representatives, respectively, of the dilute phase, the transition point, and the dense phase of the ordinary SLE. The resulting traces are shown to be scale invariant. Using two equivalent schemes, we extract the fractal dimension, D_{f}(H), of the traces which decrease monotonically with increasing H, reaching D_{f}=1 at H=1 for all κ values. The left passage probability (LPP) test demonstrates that, for H values not far from the uncorrelated case (small ε_{H}≡H-H_{BM}/H_{BM}), the prediction of the ordinary SLE is applicable with an effective diffusivity parameter κ_{eff}. Not surprisingly, the κ_{eff}'s do not fulfill the prediction of SLE for the relation between D_{f}(H) and the diffusivity parameter.

Evaluation of the properties and antibacterial activity of microchitosan film impregnated with Shirazi thyme (Zataria multiflora) and garlic (Allium sativum) essential oils

BACKGROUND

Recent research has shown that chitosan has good moisture-absorbing properties at the micro and nanoscale, and seems to be a good candidate for the production of biodegradable moisture-absorbing films.

AIMS

The aim of this study was to evaluate the properties and antibacterial activity of starch-based microchitosan (MCH) films impregnated with two essential oils (EOs).

METHODS

MCH films with varying thicknesses were made from cornstarch (6%), microchitosan (1%), glycerol (2.25%), and/or EOs (2%), and their characteristics, including swelling degree (SD), tensile strength (TS), and elongation at break (EB%), were examined. The film structures were confirmed by X-ray diffraction (XRD), scanning electron microscopy (SEM), and atomic force microscopy (AFM). To determine the antibacterial activity against Escherichia coli and Staphylococcus aureus, two EOs of Shirazi thyme, garlic, and a mixture of them were used in the experimentation.

RESULTS

The EB% and TS had a linear relationship with the thickness of samples and improved by increasing the thickness of films. The XRD pattern showed that the MCH films had an amorphous structure. SEM of the films showed a homogeneous dispersion of MCH in the starch matrix without any porosity. The AFM images showed a simultaneous increase in the thickness of the MCH films and surface roughness. The film was able to absorb water up to 15.78 times its weight in 48 h. The inhibition zone of films containing 2% thyme EO was 42.0 mm for S. aureus and 12.3 mm for E. coli (P<0.05).

CONCLUSION

MCH film containing Shirazi thyme can be described as a moisture-absorbing antibacterial pad and is a new idea for active food packaging to increase the shelf life of foods with fully degradable properties.

Superstatistical two-temperature Ising model

The previous approach of the nonequilibrium Ising model was based on the local temperature in which each site or part of the system has its own specific temperature. We introduce an approach of the two-temperature Ising model as a prototype of the superstatistic critical phenomena. The model is described by two temperatures (T_{1},T_{2}) in a zero magnetic field. To predict the phase diagram and numerically estimate the exponents, we develop the Metropolis and Swendsen-Wang Monte Carlo method. We observe that there is a nontrivial critical line, separating ordered and disordered phases. We propose an analytic equation for the critical line in the phase diagram. Our numerical estimation of the critical exponents illustrates that all points on the critical line belong to the ordinary Ising universality class.