A Human in Modern Medicine: From the Restoration of Health to Improve

The article analyzes the dynamics of the development of medical models of treatment of deviations from the health norm, discusses the issue of changing ideas about the human health in medicine. It is shown that as a result of changes in the conceptual understanding of health and the process of its restoration, the principle of achieving a commercially profitable, fast and controlled result is introduced into modern medicine, as a result of that the process of medical treatment is standardized and regulated. But the preservation of object optics of views in the medical industry, as shown in the article, becomes ineffective, moreover, risky in a situation of moving boundaries of the human health norm. To overcome the existing risks, new institutes and practices of ethical examination of health standards are being introduced into medicine. It is shown that the accepted deliberative practices of ethical expertise only introduce a procedure for taking into account the patient’s position regarding the boundaries of their health standards and the limits of medical intervention. At the same time, the patient’s position is considered as something ready, initially given, in other words, the classic “human project” continues to be defended in medicine.

Solution of boundary value problems with moving boundaries by using an approximate method for constructing solutions of integro – differential equations

The problem of oscillations of objects with moving boundaries, formulated as a differential equation with boundary and initial conditions, is a non-classical generalization of a problem of hyperbolic type. To facilitate the construction of a solution to this problem and justify the choice of a solution form, equivalent integro-differential equations are constructed with symmetric and time-dependent kernels and integration limits varying in time. The method for constructing solutions of integro-differential equations is based on the direct integration of differential equations in combination with the standard replacement of the desired function with a new variable. The method is extended to a wider class of model boundary value problems that take into account the bending stiffness of an oscillating object, the resistance of the environment, and the rigidity of the substrate. Particular attention is paid to the consideration of the most common in practice case when external disturbances act at the boundaries. The solution is made in dimensionless variables accurate to second-order values of smallness with respect to small parameters characterizing the speed of the border.

Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries

This work extends the characteristic-based volume penalization method, originally developed and demonstrated for compressible subsonic viscous flows in (J. Comput. Phys. 262, 2014), to a hyperbolic system of partial differential equations involving complex domains with moving boundaries. The proposed methodology is shown to be Galilean-invariant and can be used to impose either homogeneous or inhomogeneous Dirichlet, Neumann, and Robin type boundary conditions on immersed boundaries. Both integrated and non-integrated variables can be treated in a systematic manner that parallels the prescription of exact boundary conditions with the approximation error rigorously controlled through an a priori penalization parameter. The proposed approach is well suited for use with adaptive mesh refinement, which allows adequate resolution of the geometry without over-resolving flow structures and minimizing the number of grid points inside the solid obstacle. The extended Galilean-invariant characteristic-based volume penalization method, while being generally applicable to both compressible Navier–Stokes and Euler equations across all speed regimes, is demonstrated for a number of supersonic benchmark flows around both stationary and moving obstacles of arbitrary shape.