Simulation of oscillatory processes in the MVSTUDIUM package

The mathematical model and algorithms of oscillatory movements are considered. Various factors affecting the oscillatory process are considered. Oscillatory movements are constructed in the MVSTUDIUM modeling environment. The schemes of three computer models demonstrating oscillatory processes are determined: a model of a pendulum with a non-movable suspension point, a model of a pushing pendulum with friction force and a model of a breaking pendulum. Classes are being built to execute models with embedded properties, as well as with the ability to export the created classes to other models, and embed classes created by the program developer into the model. Creation of 2D and 3D models of oscillatory processes, an experiment behavior map and a virtual stand.

Innovation in the computer industry

A learning-curve approach has been employed to study inventiveness in the computer industry. The appearance of new models as well as the appearance of new computer manufacturers have been following typical logistic S-curves over the last 26 years of computer history. Innovation seems to come in S-waves, and even though many of today's major manufacturers are close to exhausting their maximum innovation potential in their present S-wave, the overall computer market is rather “young”. In contrast, the personal computer market is already beyond its maturity phase. Remarkably invariant over the 26 years considered, and through the complete range of computer sizes, remains the fact that for every five new computer models appearing on the market, there is one new computer company emerging also.

“The Source of Life” in Bishop’s Basilica Of Philippopolis in the Context of Steam

The main task considered in this material is related to the restoration of the mosaic “Source of Life” in the Bishop’s Basilica of Philippopolis. Ideas for creation and use of computer models of the geometric scheme and of separate figures in the considered mosaic are presented. Technologies such as 360-degree photography, 3D printing, specialized software for creating computer models, etc. are shared to provide conditions for research work. STEAM training, especially in the context of STEAM centers and innovative schools, creates good opportunities for the widespread deployment of such resources. Most of the described educational resources are provided with free access in the Virtual Mathematics Laboratory, developed at the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences.

Crack resistance of masonry walls

Computer models used in the design calculation of masonry buildings sometimes fail to correctly take into account the stress-strain state of walls and assess the likelihood of cracks caused by the deformation differences of interacting walls.Following the construction of a building, cracks can develop at wall intersections for several years. However, their repair is mostly ineffective until the total damping of masonry creep deformation.Drawing on the analysis of conducted research and field data, the authors give recommendations on ensuring the crack resistance of internal masonry walls.

ON THE EFFECTIVENESS OF OBLIQUE CAISSON REINFORCED CONCRETE FLOORS

The distribution of forces in the beams of a straight and oblique monolithic reinforced concrete caisson fl oor of a square plan is compared. The forces in the beams are determined by well-known analytical methods and using fi nite element models of the SCAD PC. The calculations showed that the forces in the beams of the oblique caisson fl oor, determined analytically and using computer models, diff er signifi cantly, which indicates the complex operation of the spatial system, which is not taken into account by the analytical calculation method based on the theory of calculating plates supported by the contour. The obtained data indicate that a square caisson fl oor with beams installed at an angle of 450 to the reference contour has greater rigidity and lower values of bending moments compared to straight caissons. When the ratio of the sides of the overlap L2 > 1,5 . L1 to ensure the eff ect of supporting the contour, the location of the beams in relation to the outer contour should be at an angle of 45°.

Mathematical Modelling of Epidemiology

In order to combat the spread of infectious diseases, scientists from a combination of fields have started to develop mathematical models to represent these diseases. With computer models and applied mathematics, one can predict and control various diseases. We present the evolution and implementation of different models used in mathematical modelling as well as a demonstration of the SIR model in MATLAB.