Community formation in wealth-mediated thermodynamic strategy evolution.

We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution, which depends on the neighborhood bank values associated with each strategy, relative to a temperature scale, which defines the random fluctuations. Players with higher bank values are, thus, less likely to change strategy than players with a lower bank value. For a parameterized rock-paper-scissors game, we derive a condition under which communities of a given strategy form with either fixed or drifting boundaries. We show the effect of a temperature increase on the underlying system and identify surprising properties of this model through numerical simulations.

Fixation in the stochastic Lotka-Volterra model with small fitness trade-offs.

We study the probability of fixation in a stochastic two-species competition model. By identifying a naturally occurring fast timescale, we derive an approximation to the associated backward Kolmogorov equation that allows us to obtain an explicit closed form solution for the probability of fixation of either species. We use our result to study fitness tradeoff strategies and show that, despite some tradeoffs having nearly negligible effects on the corresponding deterministic dynamics, they can have large implications for the outcome of the stochastic system.

Rapid Stabilization of Immiscible Fluids using Nanostructured Interfaces via Surfactant Association.

Surfactant molecules have been extensively used as emulsifying agents to stabilize immiscible fluids. Droplet stability has been shown to be increased when ordered nanoscale phases form at the interface of the two fluids due to surfactant association. Here, we report on using mixtures of a cationic surfactant and long chained alkenes with polar head groups [e.g., cetylpyridinium chloride (CPCl) and oleic acid] to create an ordered nanoscale lamellar morphology at aqueous-oil interfaces. The self-assembled nanostructure at the liquid-liquid interface was characterized using small-angle x-ray scattering, and the mechanical properties were measured using interfacial rheology. We hypothesize that the resulting lamellar morphology at the liquid-liquid interface is driven by the change in critical packing parameter when the CPCl molecules are diluted by the presence of the long chain alkenes with polar head groups, which leads to a spherical micelle-to-lamellar phase transition. The work presented here has larger implications for using nanostructured interfacial material to separate different fluids in flowing conditions for biosystems and in 3D printing technology.

Fast cheater migration stabilizes coexistence in a public goods dilemma on networks.

Through the lens of game theory, cooperation is frequently considered an unsustainable strategy: if an entire population is cooperating, each individual can increase its overall fitness by choosing not to cooperate, thereby still receiving all the benefit of its cooperating neighbors while no longer expending its own energy. Observable cooperation in naturally-occurring public goods games is consequently of great interest, as such systems offer insight into both the emergence and sustainability of cooperation. Here we consider a population that obeys a public goods game on a network of discrete regions (that we call colonies), between any two of which individuals are free to migrate. We construct a system of piecewise-smooth ordinary differential equations that couple the within-colony population dynamics and the between-colony migratory dynamics. Through a combination of analytical and numerical methods, we show that if the workers within the population migrate sufficiently fast relative to the cheaters, the network loses stability first through a Hopf bifurcation, then a torus bifurcation, after which one or more colonies collapse. Our results indicate that fast moving cheaters can act to stabilize worker-cheatercoexistence within network that would otherwise collapse. We end with a comparison of our results with the dynamics observed in colonies of the ant species Pristomyrmex punctatus, and argue that they qualitatively agree.

Modeling of cytometry data in logarithmic space: When is a bimodal distribution not bimodal?

Recent efforts in systems immunology lead researchers to build quantitative models of cell activation and differentiation. One goal is to account for the distributions of proteins from single-cell measurements by flow cytometry or mass cytometry as readout of biological regulation. In that context, large cell-to-cell variability is often observed in biological quantities. We show here that these readouts, viewed in logarithmic scale may result in two easily-distinguishable modes, while the underlying distribution (in linear scale) is unimodal. We introduce a simple mathematical test to highlight this mismatch. We then dissect the flow of influence of cell-to-cell variability proposing a graphical model which motivates higher-dimensional analysis of the data. Finally we show how acquiring additional biological information can be used to reduce uncertainty introduced by cell-to-cell variability, helping to clarify whether the data is uni- or bimodal. This communication has cautionary implications for manual and automatic gating strategies, as well as clustering and modeling of single-cell measurements. © 2018 International Society for Advancement of Cytometry.

Cyclic public goods games: Compensated coexistence among mutual cheaters stabilized by optimized penalty taxation.

We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good ("cheating"). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or "tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and untaxed cases. We then formulate an optimal taxation problem and show that it admits a quasilinearization, resulting in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second-order ordinary differential equation.

Flow instabilities due to the interfacial formation of surfactant-fatty acid material in a Hele-Shaw cell.

We present an experimental study of pattern formation during the penetration of an aqueous surfactant solution into a liquid fatty acid in a Hele-Shaw cell. When a solution of the cationic surfactant cetylpyridinium chloride is injected into oleic acid, a wide variety of fingering patterns are observed as a function of surfactant concentration and flow rate, which are strikingly different than the classic Saffman-Taylor (ST) instability. We observe evidence of interfacial material forming between the two liquids, causing these instabilities. Moreover, the number of fingers decreases with increasing flow rate Q, while the average finger width increases with Q, both trends opposite to the ST case. Bulk rheology on related mixtures indicates a gel-like state. Comparison of experiments using other oils indicates the importance of pH and the carboxylic head group in the formation of the surfactant-fatty acid material.

Transition matrix model for evolutionary game dynamics.

We study an evolutionary game model based on a transition matrix approach, in which the total change in the proportion of a population playing a given strategy is summed directly over contributions from all other strategies. This general approach combines aspects of the traditional replicator model, such as preserving unpopulated strategies, with mutation-type dynamics, which allow for nonzero switching to unpopulated strategies, in terms of a single transition function. Under certain conditions, this model yields an endemic population playing non-Nash-equilibrium strategies. In addition, a Hopf bifurcation with a limit cycle may occur in the generalized rock-scissors-paper game, unlike the replicator equation. Nonetheless, many of the Folk Theorem results are shown to hold for this model.

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games.

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Critical angle for electrically driven coalescence of two conical droplets.

Oppositely charged drops attract one another and, when the drops are sufficiently close, electrical stresses deform the leading edges of each drop into cones. We investigate whether or not the liquid cones coalesce immediately following contact. Using high-speed imaging, we find that the coalescence behavior depends on the cone angle, which we control by varying the drop size and the applied voltage across the drops. The two drops coalesce when the slopes of the cones are small, but recoil when the slopes exceed a critical value. We propose a surface energy model (volume-constrained area minimization) to describe the transition between these two responses. The model predicts a critical cone angle of 30.8 degrees , which is in good agreement with our measurements.

Cavity ripples observed during the impact of solid objects into liquids.

We report the experimental observation of a well-defined rippling of the air cavity entrained by a rapidly moving solid object entering the free surface of a liquid (water or ethanol). The ripples are fixed in the lab frame, and begin just after the pinch-off (deep seal) of the cavity, simultaneous with the acoustic emission. This acoustic resonance corresponds approximately to the Minnaert frequency for volume oscillations of the bubble. We present an irrotational model which explains the ripples as a spatial rectification of these volume oscillations by the surface of the moving object.

Fingering instabilities of a reactive micellar interface.

We present an experimental study of the fingering patterns in a Hele-Shaw cell occurring when a gel-like material forms at the interface between aqueous solutions of a cationic surfactant (cetyltrimethylammonium bromide) and an organic salt (salicylic acid), two solutions known to form a highly elastic wormlike micellar fluid when mixed homogeneously. A variety of fingering instabilities are observed, depending on the velocity of the front (the injection rate), and on which fluid is injected into which. We have found a regime of nonconfined stationary or wavy fingers for which width selection seems to occur without the presence of bounding walls, unlike the Saffman-Taylor experiment. Qualitatively, some of our observations share common mechanisms with instabilities of cooling lava flows or growing biofilms.

Motion of a viscoelastic micellar fluid around a cylinder: flow and fracture.

We present an experimental study of the motion of a viscoelastic micellar fluid around a moving cylinder, which ranges from fluidlike flow to solidlike tearing and fracture, depending on the cylinder radius and velocity. The observation of crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed.

Oscillatory rise of bubbles in wormlike micellar fluids with different microstructures.

Previous observations of the nontransient oscillations of rising bubbles and falling spheres in wormlike micellar fluids were limited to a single surfactant system. We present an extensive survey of rising bubbles in another system, an aqueous solution of cetylpyridinium chloride and sodium salicylate, with and without NaCl, across a range of concentrations and temperatures. Two different types of oscillations are seen in different concentration ranges, each with its own temperature dependence. Rheological data identify these different hydrodynamic states with different fluid microstructures.

Oscillations of a solid sphere falling through a wormlike micellar fluid.

We present an experimental study of the motion of a solid sphere falling through a wormlike micellar fluid. While smaller or lighter spheres quickly reach a terminal velocity, larger or heavier spheres are found to oscillate in the direction of their falling motion. The onset of this instability correlates with a critical value of the velocity gradient scale Gamma(c) approximately s(-1). We relate this condition to the known complex rheology of wormlike micellar fluids, and suggest that the unsteady motion of the sphere is caused by the formation and breaking of flow-induced structures.