Chaotic dynamics in a quantum Fermi-Pasta-Ulam problem

We investigate the emergence of chaotic dynamics in a quantum Fermi - Pasta - Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed.Comment: Submitted to Entrop

Determination of the Influence of Natural Antioxidant Concentrations on the Shelf Life of Sunflower Oil

The influence of natural antioxidants from different types of vegetable raw materials on the processes of oxidative and hydrolytic spoilage of sunflower oil during storage is studied. Plant antioxidants are more environmentally friendly and safer than synthetic ones.Green tea leaves and oak bark were used as vegetable raw materials. Water-ethanol extracts from vegetable raw materials were added to oil samples in experimental concentrations. The samples were stored in the laboratory conditions at the temperature of (20±2) °C. The study was performed for 5 months. The values of the acid and peroxide numbers were determined.The most effective blend of antioxidants showed the increase in the acid number from 0.12 to 0.20 mg KOH/g (concentration of green tea extract – 0.05 %, without the addition of oak bark extract).According to the values of the peroxide number, the most effective blends of antioxidants were the experiment points with the following green tea extract:oak bark extract ratio: (0.05:0.05) %, (0.025:0.025) %, (0.025:0.05) %, (0.05:0.025) %.To determine the induction period of oil and, accordingly, its shelf life under experimental conditions, the values of the peroxide numbers were used. It is rational to use extractives from oak bark and green tea under the following conditions: the concentration of each of the antioxidant extracts in terms of dry matter – (0.025‑0.04) %. The maximum induction period is 100 days.The efficiency of natural antioxidants in terms of the concentration of oak bark and green tea extracts is 0.05 and 0.025 %, respectively, was compared to the effectiveness of the corresponding concentration of one of the synthetic antioxidants – butylhydroxyanisole. When using butylhydroxyanisole, the induction period of oil was 65 days, and when using natural antioxidants – 74 day