Analytic-Numerical Modeling and Investigation of Nanostructures' Dynamics on Material Surfaces After Laser Irradiation

The work is devoted to modeling the formation and behavior of solid nano-sized particles on the surface of materials. In the simulation, it is assumed that the main processing technology of surface nanostructures is laser irradiation, which causes the Brownian motion of nanoparticles, due mainly to thermal fluctuations: if the temperature around the nanoparticles is uniformly distributed, the time average of the Brownian fluctuations is zero; however, if there is a temperature gradient around the nanoparticles, the thermal fluctuations affect the nanoparticle in different ways from different sides, and there is a force like the thermophoretic force, biasing the average position of the nanoparticle. When building a 1D model of the formation and flow behavior of nanoparticles, three important assumptions are introduced: the impact of nanoparticles on the process of irradiation is negligible; the impact of nanoparticles on each other as compared to the effect of laser irradiation on them is also negligible; and nanoparticles after laser irradiation can move both forward and backward and at every fixed period of time, moving the nanoparticles does not impose any steric constraints. Under the above assumptions, a 1D continuous model is built, implicit and explicit finite difference schemes to solve it are developed; their convergence and order of convergence are studied; an output condition ensuring the stability of the explicit difference scheme is obtained, the unconditional stability of implicit difference scheme is proven, and software for computer implementation of some of the obtained analytical and numerical results developed.

GOLD - SECTION IN INTERACTIVE USER INTERFACE DEVELOPMENT

The days when only specialists worked with programs and the functionality was the most important have long passed. In today's competitive environment, an important marketing component is reliability in which the only tangible part of the program, the interface, plays a large role. Purely psychological, it is important for the users' visibility, correctness and can even be argued, friendliness. This is determined by the elements of visibility and components' location in intuitively expected places, design integrity, tone and choice of characteristic elements which, together, create a feeling of sympathy or antipathy from the software user. Regularities, which ultimately determine the user's subconscious reactions, are found in natural formations - from the most basic proportions of plants to more sophisticated self-arranged compositions. The harmony of the structures of natural systems, that is, their internal organization, is subject to certain mathematical laws. Objective world stable stationary states corresponding to particular figures, called generalized Golen Ratios. These figures are all the structure of the invariant, which are embodied by the dialectic structure of the world and the different variations that can be observed at every step of nature. It is important to note that with the generalized Golden Ratio, not only is the well-known ratio of 1:1,618 understood, but a whole line of relationships, where like in music, a single major or minor note can be played, and another can stand out from the whole ensemble. The main applications of the Goden Ratio in interface design are space division, caption-font size ratios, restrictive areas (buttons), title queue length, color tone saturation ratio, and cell location coordinates. In this paper, we propose certain recomendations for the development of a user - friendly interface. These recommendations suggest uses in the software developer training process for non-design specialty students; target group - programmers, computer specialists, and IT project managers. The article does not address the development of graphic design tools and their functionality