Abstract

In this paper, we present a discrete model governing the deformation of a convex regular polygon subjected not to cross a given flat rigid surface, on which it initially lies in correspondence of one point only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Euclidean space. Second, we show the existence and uniqueness of the solution. The model provides a simplified illustration of processes involved in virus imaging by atomic force microscopy: adhesion to a surface, distributed strain, relaxation to a shape that balances adhesion and elastic forces. The analysis of numerical simulations results based on this model opens a new way of estimating the contact area and elastic parameters in virus contact mechanics studies.

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Dragnea Research is at the forefront of multidisciplinary innovation, exploring the intersection of nanoscale optics, quantum photonics, physical virology, and bio-architected hybrid materials with 3D nanoscale order. Their latest publications highlight groundbreaking advancements in fields such as self-assembly, optics and spectroscopy, and the physical manipulation of virus-like particles (VLPs) for chemical imaging and surface modifications. Drawing from their expertise in using near-field scanning techniques and laser-induced effects, these works showcase how nanoscale phenomena can be harnessed for applications in material science, virology, and beyond. The accompanying visual mosaic underscores the diverse range of their research, from probing molecular dynamics to the development of 3D-ordered structures, all united by a commitment to pushing the boundaries of applied and theoretical science.