arXiv subjects

Nathaniel J. Karst

Publications and source records attributed to Nathaniel J. Karst.

5 recordsLinked to original sources

arXiv2024

Spatio-Temporal Instabilities of Blood Flow in a Model Capillary Network

We present experimental evidence of multiple blood flow configurations in a relatively simple microfluidic network under constant inlet conditions. We provide evidence of multistability and unsteady dynamics and find good agreement with a theoretical {one-dimensional advection} model for blood flow in microvascular networks{ that relies on the widely used laws for rheology and phase separation}. We discuss the ramifications for microfluidic experiments and measurements using blood and implications for in vivo microcirculation. Our findings suggest that further modeling in microvascular networks should discard the usual assumption of unique, steady-state flow solutions, with crucial consequences regarding gas, nutrient, and waste transport.

physics.flu-dyn↗

arXiv2021

Analytic instability thresholds in folded Kerr resonators of arbitrary finesse

We present analytic threshold formulae applicable to both dispersive (time-domain) and diffractive (pattern-forming) instabilities in Fabry-Perot Kerr cavities of arbitrary finesse. We do so by extending the gain-circle technique, recently developed for counter-propagating fields in single-mirror-feedback systems, to allow for an input mirror. In time-domain counter-propagating systems walk-off effects are known to suppress cross-phase modulation contributions to dispersive instabilities. Applying the gain-circle approach with appropriately-adjusted cross-phase couplings extends previous results to arbitrary finesse, beyond mean-field approximations, and describes Ikeda instabilities.

nlin.PS↗

arXiv2015

Observations of spontaneous oscillations in simple two-fluid networks

We investigate the laminar flow of two-fluid mixtures inside a simple network of inter-connected tubes. The fluid system is comprised of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct phases. Downstream of a diverging network junction the two fluids do not necessarily split in equal fraction and thus heterogeneity is introduced into network. We find that in the simplest network, a single loop with one inlet and one outlet, under steady inlet conditions the flow rates and distribution of the two fluids within the network loop can undergo persistent spontaneous oscillations. We develop a simple model which highlights the basic mechanism of the instability and we demonstrate that the model can predict the region of parameter space where oscillations exist. The model predictions are in good agreement with experimental observations.

physics.flu-dyn↗

arXiv2013

Individual behavioral rules sustain the cell allocation pattern in the combs of honey bee colonies (Apis mellifera)

In the beeswax combs of honey bees, the cells of brood, pollen, and honey have a consistent spatial pattern that is sustained throughout the life of a colony. This spatial pattern is believed to emerge from simple behavioral rules that specify how the queen moves, where foragers deposit honey/pollen and how honey/pollen is consumed from cells. Prior work has shown that a set of such rules can explain the formation of the allocation pattern starting from an empty comb. We show that these rules cannot maintain the pattern once the brood start to vacate their cells, and we propose new, biologically realistic rules that better sustain the observed allocation pattern. We analyze the three resulting models by performing hundreds of simulation runs over many gestational periods and a wide range of parameter values. We develop new metrics for pattern assessment and employ them in analyzing pattern retention over each simulation run. Applied to our simulation results, these metrics show alteration of an accepted model for honey/pollen consumption based on local information can stabilize the cell allocation pattern over time. We also show that adding global information, by biasing the queen's movements towards the center of the comb, expands the parameter regime over which pattern retention occurs.

q-bio.PE↗

arXiv2013

Spontaneous oscillations in simple fluid networks

Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituent flows. In many systems, such behavior might be attributed to the complicated geometry of the network, the complex rheology of the constituent fluids, or, in the case of microvascular blood flow, biological control. In this paper we investigate two examples of a simple three-node fluid network containing two miscible Newtonian fluids of differing viscosities, the first modeling microvascular blood flow and the second modeling stratified laminar flow. We use a combination of analytic and numerical techniques to identify and track saddle-node and Hopf bifurcations through the large parameter space. In both models, we document sustained spontaneous oscillations and, for an experimentally relevant example of parameter analysis, investigate the sensitivity of these oscillations to changes in the viscosity contrast between the constituent fluids and the inlet flow rates. For the case of stratified laminar flow, we detail a physically realizable set of network parameters that exhibit rich dynamics. The tools and results developed here are general and could be applied to other physical systems.

math.DS↗