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Coordination of fate transition and cell division is crucial to maintain the plant architecture and to achieve efficient production of plant organs. In this paper, we analysed the stem cell dynamics at the shoot apical meristem (SAM) that is one of the plant stem cells locations. We designed a mathematical model to elucidate the impact of hormonal signaling on the fate transition rates between different zones corresponding to slowly dividing stem cells and fast dividing transit amplifying cells. The model is based on a simplified two-dimensional disc geometry of the SAM and accounts for a continuous displacement towards the periphery of cells produced in the central zone. Coupling growth and hormonal signaling results in a nonlinear system of reaction-diffusion equations on a growing domain with the growth rate depending on the model components. The model is tested by simulating perturbations in the level of key transcription factors that maintain SAM homeostasis. The model provides new insights on how the transcription factor HECATE is integrated in the regulatory network that governs stem cell differentiation., Author summary Plants continuously generate new organs such as leaves, roots and flowers. This process is driven by stem cells which are located in specialized regions, so-called meristems. Dividing stem cells give rise to offspring that, during a process referred to as cell fate transition, become more specialized and give rise to organs. Plant architecture and crop yield crucially depend on the regulation of meristem dynamics. To better understand this regulation, we develop a computational model of the shoot meristem. The model describes the meristem as a two-dimensional disk that can grow and shrink over time, depending on the concentrations of the signalling factors in its interior. This allows studying how the non-linear interaction of multiple transcription factors is linked to cell division and fate-transition. We test the model by simulating perturbations of meristem signals and comparing them to experimental data. The model allows simulating different hypotheses about signal effects. Based on the model we study the specific role of the transcription factor HECATE and provide new insights in its action on cell dynamics and in its interrelation with other known transcription factors in the meristem.

We consider the quasi-static evolution of thermo-visco-elastic material. The main goal of this paper is to present how taking into account the additional effects may improve the result of solutions' existence. We added a micropolarity effect to thermo-visco-elastic model regarding Norton-Hoff-type constitutive function. This additional phenomenon improves the regularity of solution. Copyright (C) 2016 John Wiley & Sons, Ltd.

We derive a thermomechanical model for the evolution of the visco-elastic body subject to the action of external forces. The presented framework captures elastic and visco-elastic deformation as well as thermal effects occurring in the material. Consequently we couple the momentum balance with the heat equation. The system is supplemented by the constitutive relation for the Cauchy stress tensor and visco-elastic strain tensor. As an example exhibiting the proposed approach one can mention the Mroz model. We establish existence of solutions to the quasi-static version of the derived system.

We study a quasi-static evolution of the thermo-visco-elastic model. We act with external forces on a non-homogeneous material body, which is a subject of our research. Such action may cause deformation of this body and may change its temperature. Mechanical part of the model contains two kinds of deformation: elastic and visco-elastic. The mechanical deformation is coupled with temperature and both of them may influence each other. Since the constitutive function on evolution of the visco-elastic deformation depends on temperature, the visco-elastic properties of material also depend on temperature. We consider the thermodynamically complete model related to a hardening rule with growth condition in generalized Orlicz spaces. We provide the proof of existence of solutions for such class of models.