arXiv subjects

Vivi Rottschäfer

Publications and source records attributed to Vivi Rottschäfer.

3 recordsLinked to original sources

arXiv2026

Laws of mutual spiral wave interaction in excitable media

Interacting rotating spiral waves have been observed in complex systems, such as cardiac fibrillation, cognitive processing in the brain cortex and oscillating chemical reactions, during dynamical regimes that are still poorly understood. We present the equivalent of Newton's gravitational attraction law for spiral waves on planar reaction-diffusion systems. The spiral waves' phases and positions determine their regions of influence, separated by collision interfaces. At the collision interfaces, wave front deflections cause spiral drift that pushes the interfaces forward. As a result, the spiral wave drift velocity is proportional to the total force exerted on on it, which can be determined by a boundary integral over its region of influence. The proportionality factor between force and response is akin to the `mass' of the spiral. However, this spiral mass depends on the region of influence of the spiral and thus also varies over time. The forces between spiral wave pairs are not directed along the line connecting their centers, violating Newton's law of action and reaction. Our solution to the N-body interaction problem for spirals in extended excitable media encompasses both pairwise interactions and spiral wave drift in bounded domains, with application to cardiac fibrillation.

nlin.PS↗

arXiv2024

Messenger size optimality in cellular communications

Living cells presumably employ optimized information transfer methods, enabling efficient communication even in noisy environments. As expected, the efficiency of chemical communications between cells depends on the properties of the molecular messenger. Evidence suggests that proteins from narrow ranges of molecular masses have been naturally selected to mediate cellular communications, yet the underlying communication design principles are not understood. Using a simple physical model that considers the cost of chemical synthesis, diffusion, molecular binding, and degradation, we show that optimal mass values exist that ensure efficient communication of various types of signals. Our findings provide insights into the design principles of biological communications and can be used to engineer chemically communicating biomimetic systems.

physics.bio-ph↗

arXiv2019

Modelling honey bee colonies in winter using a Keller-Segel model with a sign-changing chemotactic coefficient

Thermoregulation in honey bee colonies during winter is thought to be self-organised. We added mortality of individual honey bees to an existing model of thermoregulation to account for elevated losses of bees that are reported worldwide. The aim of analysis is to obtain a better fundamental understanding of the consequences of individual mortality during winter. This model resembles the well-known Keller-Segel model. In contrast to the often studied Keller-Segel models, our model includes a chemotactic coefficient of which the sign can change as honey bees have a preferred temperature: when the local temperature is too low, they move towards higher temperatures, whereas the opposite is true for too high temperatures. Our study shows that we can distinguish two states of the colony: one in which the colony size is above a certain critical number of bees in which the bees can keep the core temperature of the colony above the threshold temperature, and one in which the core temperature drops below the critical threshold and the mortality of the bees increases dramatically, leading to a sudden death of the colony. This model behaviour may explain the globally observed honey bee colony losses during winter.

q-bio.PE↗