ABSTRACT
For universality in the approach, it is customary to appropriately rescale problems to a single or a set of dimensionless equations with dimensionless quantities involved or to rescale the experimental setup to a suitable size for the laboratory conditions. Theoretical results and/or experimental findings are supposed to be valid for both the original and the rescaled problems. Here, however, we show in an analog computer model nonlinear system how the experimental results depend on the scale factor. This is because the intrinsic noise in the experimental setup remains constant as it is not affected by the scale factor. The particular case considered here offers a genuine noise-level effect in significantly altering a period-doubling cascade to chaos besides producing an expected truncated cascade. By monitoring with increasing value a significant parameter in the dynamics of the problem when searching for its solution, the system alien to the noise (or better said with a negligible noise level) follows a period-doubling cascade from period one to period two to period four to period eight and, eventually, chaos. However, if the intrinsic noise strength significantly enters the evolution, there appears a parallel sequence of period doublings different from the one found in the previous case.
ABSTRACT
PURPOSE: The relevance of the problem is caused by an increase in the number of spine-related diseases among children, including scoliosis. Currently, there are no methodologies for the treatment of scoliosis, which ensure an unambiguous positive result. The purpose of the article is to justify the spinal model as an elastic viscoplastic body for further mathematical modeling of the process of spine correction and search for its optimal conditions. METHODOLOGY: The leading approach to the study of this problem is the development of techniques for the surgical treatment of deformities of the vertebral column with the aid of an external fixation device for the spine, providing for a rigid connection of the elements of the apparatus with each other and with the spine. The rigid connection between the elements of the external fixation device increases the degree of static indeterminacy of the design, which leads to the occurrence of additional dangerous stresses in the details of the apparatus and in the vertebrae. The control actions in such devices do not provide an adequate result for the process of correction of the vertebral column. RESULTS: The main result is the substantiation of the spine model as an elastic viscoplastic body. This will allow more detailed consideration of the medical and biological features of the spine and the physical and mechanical properties of human bone and soft tissues. The proposed model will allow developing an adaptive design of the device, taking into account specific features of the organism and more effectively managing the correction process. VALUE: The materials of the article can be useful for scientists, doctors and specialists in conducting scientific research on the problem of spine deformation correction and the development of appropriate technical means.
