Volume:

Supplement:

22

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There are volumes of different nature than the gradients ( vectors ) that can be and are the source of directional information . These are the size of the tensor , such as a mechanical tension (s ) or growth rate (w). Tensor stands in the three orthogonal directions , which assume extreme values . These are the main directions of the tensor (PD - esses ) . While the vector has direction and sense , PD has only direction . The most important difference between vector and tensor , however, concerns the symmetry ; tensor is characterized by mirror symmetry . PD- esses tensors s and / or manifest themselves : in the system of cells in the meristems , the orientation division of plant cells , arranged in the spongy bone trabeculae in the behavior of the animal cells on a flexible substrate . PD- esses tensor s are particularly well placed to create a frame of reference in the development of the model physique in embryogenesis and morphogenesis , because the trajectories of PDs , usually curved , form an orthogonal system , and one of PDs is orthogonal to the surface of the body ( including the other two are tangential to surface). It is known ( to plant cells ) a linear relationship between growth rate and the pressure turgorowym volume , where the factor of proportionality is the isotropic susceptibility wall. The control is a scalar level . This relation corresponds to the level of tensor relationship between the growth rate of linear elements and the stress factor of proportionality in the form of a fourth-order tensor ( anisotropic susceptibility wall). This tensor is a set of parameters dependent on genetic information. The equation at the level of tensor tells us that the field of stress can lead to various forms of the body , depending on genetic information. Indicated are also the results of research on the reorientation of the cortical microtubules (MTC ) in the cells of the epidermis , depending on the stress and auxin . These indicate that: MTC cycle is rotational reorientation (not oscillating ) ; reorient the angular velocity depends on the orientation with respect to the PDS- Flourish , in particular cycle may be so rapid that jumps over one or both of the PDs - esses ; MTC layout depends on which PDs cycle skips ; PDSs orientation depends on the state of stress ; skip selection of PDs ( PDmax , or PDmin s , s ) depends on the level of auxin .

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