The time-fractional kinetic equation for the non-equilibrium processes

In this study, we consider the non-Markovian dynamics of the generic non-equilibrium kinetic process. We summarize the generalized master equation, the continuous and discrete forms of the time-fractional diffusion equation. Using path integral formulation, we generalized the solutions of the Markovian system to the non-Markovian for the non-equilibrium kinetic processes. Then, we obtain the time-fractional kinetic equation for the non-equilibrium systems in terms of free energy. Finally, we introduce a time-fractional equation to analyse time evolution of the open probability for the deformed voltage-gated ion-channel system as an example.

Effect of Soaking/Oven- Drying on Mechanical and Physical Properties of Birch (Betula spp.) Plywood

The objective of this study was to explore some of the physical and mechanical properties of 9-layer birch (Betula spp.) plywood with the addition of phenol-formaldehyde glue, in cases in which the cutting edges of the samples are coated with the damp-proof mastic Fibergum, and in case in which they remain unprocessed (uncoated), following a total of ten cycles of soaking/oven-drying. The properties to be determined were the bending strength (BS), modulus of elasticity in bending (MOE), thickness swelling (TS) and restore dimensions (RD), which were tested according to the European standards (EN). A linear-fractional equation and linear relationship were used for the approximation of any change in the physical and mechanical properties of the samples depending upon the number of soaking/oven-drying cycles. It was shown that the values of the properties investigated were most affected by the first soaking and drying cycle. Thereafter, BS and MOE levels decreased smoothly at a low rate, but the values of TS became stabilised. The BS and MOE values for the wet samples with coated cutting edges were higher than when they were uncoated, as the moisture levels in the former case were lower. After the first soaking of the samples with coated cutting edges, the retention values were as follows: BS at 52.8 % and 66.7 % for the major and minor axes, respectively, with the same applying to MOE at 61.9 % and 64.2 %, while TS was at 105.2 %. To clarify the phenomenon that causes a decrease of the properties, the face plies and edge structures of the initial dry samples and of the samples after the first, second and ninth soaking/oven-drying cycles were studied using the X-Ray technique.Ključne riječi

Fast High-Order Difference Scheme for the Modified Anomalous Subdiffusion Equation Based on Fast Discrete Sine Transform

The modified anomalous subdiffusion equation plays an important role in the modeling of the processes that become less anomalous as time evolves. In this paper, we consider the efficient difference scheme for solving such time-fractional equation in two space dimensions. By using the modified L1 method and the compact difference operator with fast discrete sine transform technique, we develop a fast Crank-Nicolson compact difference scheme which is proved to be stable with the accuracy of O τ min 1 + α , 1 + β + h 4 . Here, α and β are the fractional orders which both range from 0 to 1, and τ and h are, respectively, the temporal and spatial stepsizes. We also consider the method of adding correction terms to efficiently deal with the nonsmooth problems. Numerical examples are provided to verify the effectiveness of the proposed scheme.