Bridging scales in a multiscale pattern-forming system

Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another...

Quantitative analysis of surface wave patterns of Min proteins

The Min protein system is arguably the best-studied model system for biological pattern formation. It exhibits pole-to-pole oscillations in E. coli bacteria as well as a variety of surface wave patterns in in vitro reconstitutions. Such Min surface wave patterns pose particular challenges to quantification as they are typically only semi...

A multispecies cross-diffusion model for territorial development

We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for K groups instead of two groups. We then analyze this model and present two novel variations. Our model assumes that agents’ movement is a biased random walk away...

Spots, stripes, and spiral waves in models for static and motile cells: GTPase patterns in cells

The polarization and motility of eukaryotic cells depends on assembly and contraction of the actin cytoskeleton and its regulation by proteins called GTPases. The activity of GTPases causes assembly of filamentous actin (by GTPases Cdc42, Rac), resulting in protrusion of the cell edge. Mathematical models for GTPase dynamics address the...

Collective dynamics and pattern formation in systems of communicating cells: Theory and Simulations

How a system of genetically identical biological cells organizes into spatially heterogeneous tissues is a central question in biology. Even when the molecular and genetic underpinnings of cell-cell interactions are known, how these lead to multicellular patterns is often poorly understood. Of particular interest are dynamic patterns such as...

Cellular Dialogues: Cell-Cell Communication through Diffusible Molecules Yields Dynamic Spatial Patterns

Cells form spatial patterns by coordinating their gene expressions. How a group of mesoscopic numbers (hundreds to thousands) of cells, without pre-existing morphogen gradients and spatial organization, self-organizes spatial patterns remains poorly understood. Of particular importance are dynamic spatial patterns such as spiral waves that...

Provable self-organizing pattern formation by a swarm of robots with limited knowledge

In this paper we present a procedure to automatically design and verify the local behavior of robots with highly limited cognition. All robots are: anonymous, homogeneous, non-communicating, memoryless, reactive, do not know their global position, do not have global state information, and operate by a local clock. They only know: (1) the...

The PageRank algorithm as a method to optimize swarm behavior through local analysis

This work proposes PageRank as a tool to evaluate and optimize the global performance of a swarm based on the analysis of the local behavior of a single robot. PageRank is a graph centrality measure that assesses the importance of nodes based on how likely they are to be reached when traversing a graph. We relate this, using a microscopic...

Spatial organization in nano-sculptured bacteria, a tale of shape, scale, patterns, and genomes

One of the most basic features that pervade biology is the existence of boundaries that separate living cells from their outer environments. Molecules responsible for the internal organization of a living cell must adapt to its boundaries, as the cell grows, divides, and changes in shape and size. In this thesis, we aim to understand how...

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a ‘wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This ‘wave-like’ profile...

Channel and shoal development in a short tidal embayment: An idealized model study

In many tidal embayments, complex patterns of channels and shoals are observed. To gain a better understanding of these features, an idealized model, that describes the interaction of water motion, sediment transport and bed evolution in a semi-enclosed, rectangular basin, is developed and analysed. To explain the initial formation of channels...

Electromagnetically driven dwarf tornados in turbulent convection

Motivated by the concept of interdependency of turbulent flow and electromagnetic fields inside the spiraling galaxies, we explored the possibilities of generating a localized Lorentz force that will produce a three-dimensional swirling flow in weakly conductive fluids. Multiple vortical flow patterns were generated by combining arrays of...

Long-term morphodynamic evolution and energy dissipation in a coastal plain, tidal embayment

The morphodynamic system in alluvial, coastal plain estuaries is complex and characterized by various timescales and spatial scales. The current research aims to investigate the interaction between these different scales as well as the estuarine morphodynamic evolution. Use is made of a process-based, numerical model describing 2-D shallow water...

Turbulence characteristics in sharp open-channel bends

In spite of its importance, little is known about the turbulence characteristics in open-channel bends. This paper reports on an experimental investigation of turbulence in one cross section of an open-channel bend. Typical flow features are a bicellular pattern of cross-stream circulation (secondary flow) and a turbulence activity in the outer...