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There are no systematic approaches available in current specialist literature when it comes to the optimization of the process of drying out hardwood species of wood, such as birch, aspen, or black alder, all of which find industrial uses in Estonia. In order to investigate the drying of these three hardwood species, this paper has made use of an experimental and theoretical drying optimization methodology which was developed previously for pine sapwood within the framework of the EIC Grant No. 16200 project. The same methodology was used to determine the critical diffusion coefficient and corresponding critical relative humidity levels (RH) in relation to the surrounding air, with those levels being important from the point of view of drying optimization, and calculating those levels separately for each species of hardwood. For alder it was found that the critical diffusion coefficient is Dcr = 36.57 * (10−4 mm2 s−1), while for aspen the figure was Dcr = 30.71 * (10−4 mm2 s−1), and for birch it was Dcr = 16.35 * (10−4 mm2 s−1). It was found that the time dependencies for the total deformation of different tree species tend to differ considerably, although the same drying regime was used for all of those tree species which were incorporated into the experiments.

There are no systematic approaches available in current specialist literature when it comes to the optimization of the process of drying out hardwood species of wood, such as birch, aspen, or black alder, all of which find industrial uses in Estonia. In order to investigate the drying of these three hardwood species, this paper has made use of an experimental and theoretical drying optimization methodology which was developed previously for pine sapwood within the framework of the EIC Grant No. 16200 project. The same methodology was used to determine the critical diffusion coefficient and corresponding critical relative humidity levels (RH) in relation to the surrounding air, with those levels being important from the point of view of drying optimization, and calculating those levels separately for each species of hardwood. For alder it was found that the critical diffusion coefficient is Dcr = 36.57 * (10−4 mm2 s−1), while for aspen the figure was Dcr = 30.71 * (10−4 mm2 s−1), and for birch it was Dcr = 16.35 * (10−4 mm2 s−1). It was found that the time dependencies for the total deformation of different tree species tend to differ considerably, although the same drying regime was used for all of those tree species which were incorporated into the experiments. [ABSTRACT FROM AUTHOR]

The purpose of this work is to find the region of necessary and sufficient conditions for diffusion instability on the parameter plane (τ, d) of the Gierer–Meinhardt system, where τ is the relaxation parameter, d is the dimensionless diffusion coefficient; to derive analytically the dependence of the critical wave number on the characteristic size of the spatial region; to obtain explicit representations of secondary spatially distributed structures, formed as a result of bifurcation of a spatially homogeneous equilibrium position, in the form of series in degrees of supercriticality. Methods. To find the region of Turing instability, methods of linear stability analysis are applied. To find secondary solutions (Turing structures), the Lyapunov– Schmidt method is used in the form developed by V. I. Yudovich. Results. Expressions for the critical diffusion coefficient in terms of the eigenvalues of the Laplace operator for an arbitrary bounded region are obtained. The dependence of the critical diffusion coefficient on the characteristic size of the region is found explicitly in two cases: when the region is an interval and a rectangle. Explicit expressions for the first terms of the expansions of the secondary stationary solutions with respect to the supercriticality parameter are constructed in the one-dimensional case, as well as for a rectangle, when one of the wave numbers is equal to zero. In these cases, sufficient conditions for a soft loss of stability are found, and examples of secondary solutions are given. Conclusion. A general approach is proposed for finding the region of Turing instability and constructing secondary spatially distributed structures. This approach can be applied to a wide class of mathematical models described by a system of two reaction–diffusion equations.

This article demonstrates that it is possible to optimize the drying process for pine wood in two independent ways. Those ways involve either the use of the critical diffusion coefficient (DC) which is determined by the experiment shown below, and/or the drying air moistening impulse in the second drying phase. When processing data which has been gained from the pine wood drying experiment, both coincidences and differences were found when compared to the results from a simulation of the drying process which was carried out using the same drying schedule. There is a relatively good level of agreement between the drying experiment and the simulation results of TORKSIM v5.11 simulation program in the case of the simulated and experimentally determined drying curves. The magnitude of numerical values for the DC agrees with this finding, as do the wood's moisture profile in the final phase of the drying experiment at 142 hours, the simulated and measured wood surface temperatures from the beginning of drying to a point at 60 hours into the process, and the simulated wood stresses when compared with the maximum values for the electrical surface-core ratio (ESCR) graph, as determined by the experiment. It was found that the DC's numerical value decreases sharply by about 1.5 times after transitioning from the first drying phase to the second drying phase.

This article demonstrates that it is possible to optimize the drying process for pine wood in two independent ways. Those ways involve either the use of the critical diffusion coefficient (DC) which is determined by the experiment shown below, and/or the drying air moistening impulse in the second drying phase. When processing data which has been gained from the pine wood drying experiment, both coincidences and differences were found when compared to the results from a simulation of the drying process which was carried out using the same drying schedule. There is a relatively good level of agreement between the drying experiment and the simulation results of TORKSIM v5.11 simulation program in the case of the simulated and experimentally determined drying curves. The magnitude of numerical values for the DC agrees with this finding, as do the wood's moisture profile in the final phase of the drying experiment at 142 hours, the simulated and measured wood surface temperatures from the beginning of drying to a point at 60 hours into the process, and the simulated wood stresses when compared with the maximum values for the electrical surface-core ratio (ESCR) graph, as determined by the experiment. It was found that the DC's numerical value decreases sharply by about 1.5 times after transitioning from the first drying phase to the second drying phase. [ABSTRACT FROM AUTHOR]