Intervention-based stochastic disease eradication.

Disease control is of paramount importance in public health, with infectious disease extinction as the ultimate goal. Although diseases may go extinct due to random loss of effective contacts where the infection is transmitted to new susceptible individuals, the time to extinction in the absence of control may be prohibitively long. Intervention controls are typically defined on a deterministic schedule.

A mechanochemical model for auto-regulation of lung airway surface layer volume.

We develop a proof-of-principle model for auto-regulation of water volume in the lung airway surface layer (ASL) by coupling biochemical kinetics, transient ASL volume, and homeostatic mechanical stresses. The model is based on the hypothesis that ASL volume is sensed through soluble mediators and phasic stresses generated by beating cilia and air drag forces. Model parameters are fit based on the available data on human bronchial epithelial cell cultures.

Noise Induced Pattern Switching in Randomly Distributed Delayed Swarms.

We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the stability of a class of emerging patterns depends upon all moments of the time delay distribution, and predicts their bifurcation parameter ranges. Near the bifurcations of these patterns, noise may induce a transition from one type of pattern to another.

Statistical multimoment bifurcations in random-delay coupled swarms.

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.

Multicomponent hydrodynamic model for heterogeneous biofilms: two-dimensional numerical simulations of growth and interaction with flows.

We develop a tricomponent (ternary) hydrodynamic model for multiphase flows of biomass and solvent mixtures, which we employ to simulate biofilm. In this model, the three predominant effective components in biofilms, which are the extracellular polymeric substance (EPS) network, the bacteria, and the effective solvent (consisting of the solvent and nutrient, etc.), are modeled explicitly.

Spatial Stress and Strain Distributions of Viscoelastic Layers in Oscillatory Shear.

One of the standard experimental probes of a viscoelastic material is to measure the response of a layer trapped between parallel surfaces, imposing either periodic stress or strain at one boundary and measuring the other. The relative phase between stress and strain yields solid-like and liquid-like properties, called the storage and loss moduli, respectively, which are then captured over a range of imposed frequencies. Rarely are the full spatial distributions of shear and normal stresses considered, primarily because they cannot be measured except at boundaries and the information was not deemed of particular interest in theoretical studies.

Randomly Distributed Delayed Communication and Coherent Swarm Patterns.

Previously we showed how delay communication between globally coupled self-propelled agents causes new spatio-temporal patterns to arise when the delay coupling is fixed among all agents [1]. In this paper, we show how discrete, randomly distributed delays affect the dynamical patterns. In particular, we investigate how the standard deviation of the time delay distribution affects the stability of the different patterns as well as the switching probability between coherent states.

Modeling synchronization in networks of delay-coupled fiber ring lasers.

We study the onset of synchronization in a network of N delay-coupled stochastic fiber ring lasers with respect to various parameters when the coupling power is weak. In particular, for groups of three or more ring lasers mutually coupled to a central hub laser, we demonstrate a robust tendency toward out-of-phase (achronal) synchronization between the N-1 outer lasers and the single inner laser. In contrast to the achronal synchronization, we find the outer lasers synchronize with zero-lag (isochronal) with respect to each other, thus forming a set of N-1 coherent fiber lasers.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology.

The classical oscillatory shear wave model of Ferry et al. [J. Polym.