Related papers: How to grow a flat leaf

A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two…

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through…

An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a qualitative model for the growing structure involving the amplification, rectification, and advection of slack in the presence of a steady…

Attempts to understand the dynamics of warped astrophysical discs have garnered significant attention, largely motivated by the growing catalogue of observed distorted systems. Previous studies have shown that the evolution of the warp is…

Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…

A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of…

The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…

We study the peculiar wrinkling pattern of an elastic plate stamped into a spherical mold. We show that the wavelength of the wrinkles decreases with their amplitude, but reaches a maximum when the amplitude is of the order of the thickness…

Neutrino-neutrino refraction leads to collective flavor evolution that can include fast flavor conversion, an ingredient still missing in numerical simulations of core-collapse supernovae. We provide a theoretical framework for the linear…

We study the thermally assisted relaxation of a directed elastic line in a two dimensional quenched random potential by solving numerically the Edwards-Wilkinson equation and the Monte Carlo dynamics of a solid-on-solid lattice model. We…

Understanding thin sheets, ranging from the macro to the nanoscale, can allow control of mechanical properties such as deformability. Out-of-plane buckling due to in-plane compression can be a key feature in designing new materials. While…

In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…

In classification and forecasting with tabular data, one often utilizes tree-based models. Those can be competitive with deep neural networks on tabular data and, under some conditions, explainable. The explainability depends on the depth…

Multi-filamentation opens new degrees of freedom for manipulating electromagnetic waves in air. However, without control, multiple filament interactions, including attraction, repulsion or fusion often result in formation of complex…

Plant organ outgrowth superficially appears like the continuous mechanical deformation of a sheet of cells. Yet, how precisely cells as individual mechanical entities can act to morph a tissue reliably and efficiently into three dimensions…

We use numerical simulations to show how a fully flexible filament binding to a deformable cylindrical surface may acquire a macroscopic persistence length and a helical conformation. This is a result of the nontrivial elastic response to…

It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…

Biological growth is often driven by mechanical cues, such as changes in external pressure or tensile loading. Moreover, it is well known that many living tissues actively maintain a preferred level of mechanical internal stress, called the…

Natural Language Feedback (NLF) is an increasingly popular mechanism for aligning Large Language Models (LLMs) to human preferences. Despite the diversity of the information it can convey, NLF methods are often hand-designed and arbitrary,…

We study the relaxation of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated…