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This article offers a comprehensive overview of the results obtained through numerical methods in solving the minimal surface equation, along with exploring the applications of minimal surfaces in science, technology, and architecture. The content is enriched with practical examples highlighting the diverse applications of minimal surfaces.

Two mathematical models of an amperometric bienzyme biosensor are analysed digitally. The models hold different boundary conditions describing the singularity of the electrode (transducer). The influence of the initial and boundary conditions on the biosensors action at different sets of parameters is analysed.

The paper addresses the over-saturated protein spot detection and extraction problem in two-dimensional electrophoresis gel images. The effective technique for detection and reconstruction of over-saturated protein spots is proposed. The paper presents: an algorithm of the median filter mask adaptation for initial filtering of gel image; the models of over-saturation used for gel image analysis; several models of protein spots used for reconstruction; technique of the automatic over-saturated protein spot search and reconstruction. Experimental investigation confirms that proposed search technique lets to find up to 96% of over-saturated protein spots. Moreover the proposed flexible protein spot shape models for reconstruction are faster and more accurate in comparison to the flexible diffusion model.

A model of the moisture diffusion in wood under isothermal conditions taking into consideration coating of the surface of a specimen is presented in a 2-D-in-space formulation. A reliability of a corresponding 1-D model is investigated for a simulation of moisture movement in 2-D medium. This paper presents a technique to determine the width as well as the degree of edges coating of the specimen making the 1-D model relevant for 2-D medium. This technique bases on the computer simulation of 2-D moisture diffusion to estimate the reliability of the corresponding 1-D model. In the technique, approximate coefficients of the diffusion and surface emission may be employed if accurate values of these coefficients are unknown.

In this paper we consider the numerical solution of the large system of nonlinear differential equations. We assume that the system simulates the semiconductor circuit. We apply the well known event driven techniques to get some approximation of solution fast. We extend those techniques by considering pairs of nodes, instead of single nodes, as usual. The “pairwise” solution is more efficient in tightly coupled circuits. The improvement of efficiency of solution is important optimizing the parameters of circuits. In many cases we need the global optimization of equation parameters. Then, the modeling speed could be the main factor of successful application.