The mathematical model of the bronchial tree developed by the authors includes alveolar sacs. Alveolar sacs begin to appear in the human bronchial tree starting from the 15th generation of bronchi. Their number increases geometrically as they move down the bronchial tree, reaching a maximum in the terminal bronchi. The total number of sacs is more than 500 million. Human respiratory physiology imposes a number of conditions on the mathematical model of alveolar respiration. These conditions are uniform ventilation of the alveoli and minimal work associated with breathing. Therefore, the model must satisfy the condition of equal pressure in all 500 million alveolar sacs. Based on these conditions, a model of human alveolar inhalation was constructed. The alveolar pressure during inhalation, as determined in the model, is lower than atmospheric pressure, which is consistent with physiological data. Based on this model, calculations were made of the deposition of anthropogenic particles (cement dust and soot) in the lungs, which allows the risks to the respiratory system to be assessed. It has been shown that a decrease in air flow velocity (a decrease in inhaled air flow) contributes to an increase in particle deposition in the upper parts of the lungs. An increase in inhaled air flow reduces particle deposition, but at the same time, particles are "driven" into the lower parts of the lungs. Particle density has a negligible effect on their deposition compared to particle size and air flow velocity.
The field of disturbances from a school of commercial fish moving at a constant depth is investigated. The fluid is considered to be ideal and uniformly stratified. A school of fish is modeled by a group of identical point mass sources. The sources move horizontally and rectilinearly at the same speed or along the same sinusoidal trajectories with a random phase shift. A 90-degree rotation of the flock is also simulated. It is found that the result of solving the problem differs significantly from the known asymptotics near the flock, as well as in the case of rapid changes in the speed of motion of the flock, while the motion of fish along sinusoidal trajectories has little effect on the character of disturbances compared to rectilinear motion. The effect of the change in the distance between the fishes on the velocity fields of the fluid is studied. A significant influence of the distance between fish in a flock on the disturbance pattern is found at distances of the order of several flock sizes, whereas in the far zone, the disturbance pattern of the fluid does not depend on the distance between the fish and is similar to the disturbance pattern from a point mass source.
Collaboration of robotic complex and a human operator sets a task of prevention of contacts and collides between robotic links and human body. To solve this task one needs to know not only their positions at every moment but also a prediction for a certain time interval. However, control programs and motion laws fulfilled by the programs may be known not for all the parts of a robotic complex. In this article the method of prediction of a robotic complex link position is developed that does not demand a priori information on the complex structure and links motion laws. The method is based on so-called canonization of matrixes constructed from the accumulated information on previous link positions. Canonization means evaluation of matrix zero and unit devisors. The method is applicable to robotic complexes with linear control systems. The set of functions in Matlab environment are developed to evaluate the prediction. The examples of simulation for some robotic structures are given.
Authors research the task of aluminum plate geometric parameters at excision of surface layer material on both sides of considering billet. This allows us to use the hypothesis of the identity of the areas of the regions of considering stresses. The authors propose a nonstandard approach to residual stresses identification for different variants of removing the surface layer with researching billet into account transformations in the residual stress diagram. They take into account the transformation of the residual stress diagram type at changing the thickness of the aluminum billet. The known theoretical provisions on the type of residual stress diagram and the standard integral mathematical apparatus are the basis of the proposed approach. This allows us to build a mathematical model of changing the type of residual stress diagram depending on the thickness of the surface layer removal of the research aluminum plate. The authors research the change in the geometry of the studied workpiece taking into account the correction of the parameters of the residual stress diagram. This makes it possible to use the hypothesis of the equality of the areas of compressive and tensile residual stresses. The obtained results clarify the known theoretical provisions on changing the residual stress diagram after mechanical processing of the studied workpieces made of aluminum alloys.
The peculiarity of mapping the memory of the central processing unit (CPU) to the memory of the graphics processing unit (GPU) is discussed in the case of its dynamic allocation using OpenACC directives. The problem is that the array is not placed contiguously in memory. Therefore, the program associates all bytes of the computer's RAM between the start and end elements of the dynamic array with bytes of the GPU's memory, regardless of whether all of these bytes are actually occupied by the array elements. This leads to an unjustified and unpredictable increase in the size of the GPU memory allocated to store the dynamic array. Our simulations show that the increase in memory size can reach two orders of magnitude. The source code for dynamic allocation of a contiguous block of memory for two-dimensional arrays in C is given. This approach can be easily generalized to the case of an arbitrary number of dimensions. Testing of the described method showed that the sizes of dynamic arrays in the memory of the central and graphic processors coincide.
