Diffusive effects in local instabilities of a baroclinic axisymmetric vortex

We present a local stability analysis of an idealized model of the stratified vortices that appear in geophysical settings. The base flow comprises an axisymmetric vortex with background rotation and an out-of-plane stable stratification, and a radial stratification in the thermal wind balance with the out-of-plane momentum gradient. Solving the local stability equations along fluid particle trajectories in the base flow, the dependence of short-wavelength instabilities on the Schmidt number $Sc$ (ratio between momentum and mass diffusivities) is studied, in the presence of curvature effects. In the diffusion-free limit, the well-known symmetric instability is recovered. In the viscous, double-diffusive regime, instability characteristics are shown to depend on three non-dimensional parameters (including $Sc$ ), and two different instabilities are identified: (i) a monotonic instability (same as symmetric instability at $Sc = 1$ ), and (ii) an oscillatory instability (absent at $Sc = 1$ ). Separating the base flow and perturbation characteristics, two each of base flow and perturbation parameters (apart from $Sc$ ) are identified, and the entire parameter space is explored for the aforementioned instabilities. In comparison with $Sc = 1$ , monotonic and oscillatory instabilities are shown to significantly expand the instability region in the space of base flow parameters as $Sc$ moves away from unity. Neutral stability boundaries on the plane of $Sc$ and a modified gradient Richardson number are then identified for both these instabilities. In the absence of curvature effects, our results are shown to be consistent with previous studies based on normal mode analysis, thus establishing that the local stability approach is well suited to capturing symmetric and double-diffusive instabilities. The paper concludes with a discussion of curvature effects, and the likelihood of monotonic and oscillatory instabilities in typical oceanic settings.

Effect of Nonreciprocal Forces on the Stability of Dust Clusters

Results are presented from studies of the stability of the plane dust clusters in the form of a regular polygon with the number of particles from two to five. It is assumed that the particles are placed in the plasma consisting of Maxwellian electrons and a directed flow of cold ions. It is shown that, in such clusters, the oscillatory instabilities can develop along with the aperiodic instabilities. The ranges of plasma parameters are determined, within which the oscillatory instability of the five-particle cluster becomes saturated at the weakly nonlinear stage. As a result, the cluster forms a time crystal, which can be a chiral crystal.

How signalling games explain mimicry at many levels: from viral epidemiology to human sociology

Mimicry is exhibited in multiple scales, ranging from molecular, to organismal, and then to human society. ‘Batesian’-type mimicry entails a conflict of interest between sender and receiver, reflected in a deceptive mimic signal. ‘Müllerian’-type mimicry occurs when there is perfect common interest between sender and receiver in a particular type of encounter, manifested by an honest co-mimic signal. Using a signalling games approach, simulations show that invasion by Batesian mimics will make Müllerian mimicry unstable, in a coevolutionary chase. We use these results to better understand the deceptive strategies of SARS-CoV-2 and their key role in the COVID-19 pandemic. At the biomolecular level, we explain how cellularization promotes Müllerian molecular mimicry, and discourages Batesian molecular mimicry. A wide range of processes analogous to cellularization are presented; these might represent a manner of reducing oscillatory instabilities. Lastly, we identify examples of mimicry in human society that might be addressed using a signalling game approach.

Localised signalling compartments in 2D coupled by a bulk diffusion field: Quorum sensing and synchronous oscillations in the well-mixed limit

We analyse oscillatory instabilities for a coupled partial-ordinary differential equation (PDE-ODE) system modelling the communication between localised spatially segregated dynamically active signalling compartments that are coupled through a passive extracellular bulk diffusion field in a bounded 2D domain. Each signalling compartment is assumed to secrete a chemical into the extracellular medium (bulk region), and it can also sense the concentration of this chemical in the region around its boundary. This feedback from the bulk region, resulting from the entire collection of cells, in turn modifies the intracellular dynamics within each cell. In the limit where the signalling compartments are circular discs with a small common radius ɛ ≪ 1 and where the bulk diffusivity is asymptotically large, a matched asymptotic analysis is used to reduce the dimensionless PDE–ODE system into a nonlinear ODE system with global coupling. For Sel’kov reaction kinetics, this ODE system for the intracellular dynamics and the spatial average of the bulk diffusion field are then used to investigate oscillatory instabilities in the dynamics of the cells that are triggered due to the global coupling. In particular, numerical bifurcation software on the ODEs is used to study the overall effect of coupling defective cells (cells that behave differently from the remaining cells) to a group of identical cells. Moreover, when the number of cells is large, the Kuramoto order parameter is computed to predict the degree of phase synchronisation of the intracellular dynamics. Quorum sensing behaviour, characterised by the onset of collective behaviour in the intracellular dynamics as the number of cells increases above a threshold, is also studied. Our analysis shows that the cell population density plays a dual role of triggering and then quenching synchronous oscillations in the intracellular dynamics.

How Signaling Games Explain Mimicry at Many Levels: From Viral Epidemiology to Human Sociology

Mimicry is exhibited in multiple scales, ranging from molecular, to organismal, and then to human society. ‘Batesian’ type mimicry entails a conflict of interest between sender and receiver, reflected in a deceptive mimic signal. ‘Mullerian’ type mimicry occurs when there is perfect common interest between sender and receiver, manifested by an honest co-mimic signal. Using a signaling games approach, simulations show that invasion by Batesian mimics will make Mullerian mimicry unstable, in a coevolutionary chase. We use these results to better understand the deceptive strategies of SARS-CoV-2 and their key role in the COVID-19 pandemic. At the biomolecular level, we explain how cellularization promotes Mullerian molecular mimicry, and discourages Batesian molecular mimicry. A wide range of processes analogous to cellularization are presented; these might represent a manner of reducing oscillatory instabilities. Lastly, we identify examples of mimicry in human society, that might be addressed using a signaling game approach.

Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments

Initially straight slender elastic filaments and rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is known that beyond a critical value of this pre-stress, clamped rods transition to bent, twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such pre-stressed, initially twisted filaments subject to active follower forces and dissipative fluid drag. We find that degree of boundary constraint and the directionality of active forces determines if oscillatory instabilities can arise. When filaments are clamped at one end and pinned at the other with follower forces directed towards the clamped end, stable planar flapping oscillations result; reversing the directionality of the active forces quenches the instability. When both ends are clamped however, computations reveal a novel secondary instability wherein planar oscillations are destabilized by off-planar perturbations resulting in three-dimensional swirling patterns with periodic flips. These swirl-flip transitions are characterized by two distinct and time-scales. The first corresponds to unidirectional swirling rotation around the end-to-end axis. The second captures the time between flipping events when the direction of swirling reverses. We find that this spatiotemporal dance resembles relaxation oscillations with each cycle initiated by a sudden jump in torsional deformation and then followed by a period of gradual decrease in net torsion until the next cycle of variations. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by non-conservative active forces. Practically, our results suggest avenues by which pre-stress, elasticity and activity may be used to design synthetic fluidic elements to pump or mix fluid at macroscopic length scales.