Related papers: Role of curvature and domain shape on Turing patte…
Structure of the spin-orbit coupling varies from material to material and thus finding the correct spin-orbit coupling structure is an important step towards advanced spintronic applications. We show theoretically that the curvature in a…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
Coordinated cellular movements are key processes in tissue morphogenesis. Using a cell-based modeling approach we study the dynamics of epithelial layers lining surfaces with constant and varying curvature. We demonstrate that extrinsic…
We consider the impact of surface hydrodynamics on the interplay between curvature and composition in coarsening processes on model systems for biomembranes. This includes scaling laws and equilibrium configurations, which are investigated…
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…
From the striped coats of zebras to the ripples in windblown sand, the natural world abounds with locally banded patterns. Such patterns have been of great interest throughout history, and, in the last twenty years, scientists in a wide…
Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…
Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length-scales are involved has not…
We investigate the orientation of nonlinear stripe patterns in finite domains. Motivated by recent experiments, we introduce a control parameter drop from supercritical inside a domain to subcritical outside without boundary conditions at…
Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved…
The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be…
Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…
Morphogenesis emerges from dynamic feedback among geometry, mechanics, and chemistry; however, disentangling these contributions in living systems remains challenging. Here, we focus on the interplay between geometry and mechanics by…
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically…
Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…
The influence of the surface curvature on the surface tension of small droplets at equilibrium with a surrounding vapour, or small bubbles at equilibrium with a surrounding liquid, can be expanded as {\gamma}(R) = {\gamma}(planar) - .../R +…
The shapes of cell membranes are largely regulated by membrane associated, curvature active, proteins. We use a numerical model of the membrane with elongated membrane inclusions, recently developed by us, which posses spontaneous…
We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain…