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Generative models are revolutionizing materials discovery by enabling inverse design-direct generation of structures from desired properties. However, existing approaches often struggle to ensure inherent stability and symmetry while…
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An exact mapping of the tight-binding Hamiltonian for a graphene's nanoribbon under any armchair uniaxial strain into an effective one-dimensional system is presented. As an application, for a periodic modulation we have found a gap opening…
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Many biological processes and objects can be described by fractals. The paper uses a new type of objects - blinking fractals - that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that…
Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems. Despite this fact, the construction of these maps remains elusive and is primarily left to simple motivating examples. In this…
We show that, in contrast to classical random graph models, many real-world complex systems -- including a variety of biological regulatory networks and technological networks such as the internet -- spontaneously self-organize to a richly…
This work introduces a reduced-order model for plate structures with periodic micro-structures by coupling self-consistent clustering analysis (SCA) with the Lippmann-Schwinger equation, enabling rapid multiscale homogenisation of…
We investigate the conformational properties of a multi-branched polymer structure with a dendrimer-like topology, known as a snowflake polymer. This polymer is characterized by two parameters: $f_s$, which represents the functionality of…
Stomata play a crucial role in regulating plant physiological processes and reflecting environmental responses. However, accurate and high-throughput stomatal phenotyping remains challenging, as conventional approaches rely on destructive…
An activator-inhibitor-substrate model of side-branching used in the context of pulmonary vascular and lung development is considered on the supposition that spatially localized concentrations of the activator trigger local side-branching.…
Tendrils coil their shape to anchor the plant to supporting structures, allowing vertical growth toward light. Although climbing plants have been studied for a long time, extracting information regarding the relationship between the…
High-angular resolution observations at sub-millimeter/millimeter wavelengths of disks surrounding young stars have shown that their morphology is made of azimuthally-symmetric or point-symmetric substructures, in some cases with spiral…
We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…
The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify…
Consider a system of $m$ balanced linear equations in $k$ variables with coefficients in $\mathbb{F}_q$. If $k \geq 2m + 1$, then a routine application of the slice rank method shows that there are constants $\beta,\gamma \geq 1$ with…
Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and Pfluger's columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of…
We study a one dimensional model of gravitational instability in an Einstein-de Sitter universe. Scaling in both space and time results in an autonomous set of coupled Poisson-Vlasov equations for the field and phase space density, and the…