Related papers: Growth Mode Selection of Radially Growing Turing P…
The linear spline growth model (LSGM), which approximates complex patterns using at least two linear segments, is a popular tool for examining nonlinear change patterns. Among such models, the linear-linear piecewise change pattern is the…
The growth of confined magnetic films with ferromagnetic interactions between nearest-neighbor spins is studied in a stripped $(1+1)-$dimensional rectangular geometry. Magnetic films are grown irreversibly by adding spins at the boundaries…
A collection of thin structures buckle, bend, and bump into each-other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will…
We study the equilibrium configurations related to the growth of an elastic fibre in a confining flexible ring. This system represents a paradigm for a variety of biological, medical, and engineering problems. We consider a simplified…
We study the morphology of magnetic domain growth in disordered three dimensional magnets. The disordered magnetic material is described within the random-field Ising model with a Gaussian distribution of local fields with width $\Delta$.…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
The problem of morphogenesis and Turing instability are revisited from the point of view of dimensionality effects. First the linear analysis of a generic Turing model is elaborated to the case of multiple stationary states, which may lead…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids,…
We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…
The wavelength of a periodic spatial structure of Turing type is an intrinsic property of the considered reaction-diffusion dynamics and we address the question of its control at the microscopic scale for given dynamical parameters. The…
In this work, we present and analyze a general framework for vegetation dynamics in arid and semi-arid ecosystems in which non-local interactions are purely competitive. The generality of the formulation enables a systematic search for…
Systems that exhibit pattern formation are typically driven and dissipative. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum…
The irreversible growth of a magnetic film with spins having two possible orientations is studied in three-dimensional confined geometries of size $L\times L\times M$, where $M\gg L$ is the growing direction. A competing situation with two…
A direct transient growth analysis for three-dimensional perturbations to flow past a periodic array of T-106/300 low-pressure turbine fan blades is presented. The methodology is based on a singular value decomposition of the flow evolution…
Natural slender structures, such as plant leaves, petals, and tendrils, often exhibit complex three-dimensional (3D) morphologies-including twisting, helical coiling, and saddle-bending-driven by differential growth. The resulting internal…
We suggest a new focus for turbulence studies -- multi-mode correlations -- which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such…