Stable Heterogeneity for the Production of Diffusible Factors in Cell Populations

The production of diffusible molecules that promote survival and growth is common in bacterial and eukaryotic cell populations, and can be considered a form of cooperation between cells. While evolutionary game theory shows that producers and non-producers can coexist in well-mixed populations, there is no consensus on the possibility of a stable polymorphism in spatially structured populations where the effect of the diffusible molecule extends beyond one-step neighbours. I study the dynamics of biological public goods using an evolutionary game on a lattice, taking into account two assumptions that have not been considered simultaneously in existing models: that the benefit of the diffusible molecule is a non-linear function of its concentration, and that the molecule diffuses according to a decreasing gradient. Stable coexistence of producers and non-producers is observed when the benefit of the molecule is a sigmoid function of its concentration, while strictly diminishing returns lead to coexistence only for very specific parameters and linear benefits never lead to coexistence. The shape of the diffusion gradient is largely irrelevant and can be approximated by a step function. Since the effect of a biological molecule is generally a sigmoid function of its concentration (as described by the Hill equation), linear benefits or strictly diminishing returns are not an appropriate approximations for the study of biological public goods. A stable polymorphism of producers and non-producers is in line with the predictions of evolutionary game theory and likely to be common in cell populations

Zero-one survival behavior of cyclically competing species

Coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey a surprisingly simple, though non-trivial behavior. Within a model where coexistence is neutrally stable, we demonstrate a robust zero-one law: When the interactions between the three species are (generically) asymmetric, the `weakest' species survives at a probability that tends to one for large population sizes, while the other two are guaranteed to extinct. We rationalize our findings from stochastic simulations by an analytic approach.Comment: 4 pages, 3 figure

The Supply Side Determinants of Territory and Conflict

What determines the geographic extent of territory? We microfound and extend Boulding’s “Loss of Strength Gradient” to predict the extensive and intensive margins of conflict across space. We show how economies of scale in the production of violence and varying costs of projecting violence at a distance combine to affect the geographic distribution of conflict and territory. We test and probe the boundaries of this model in an experiment varying the fixed costs of conflict entry. As predicted, higher fixed costs increase the probability of exclusive territories; median behavior closely tracks equilibrium predictions in all treatments

Flow characterisation of transpiring porous media for hypersonic vehicles

This paper experimentally examines the internal and external flow characteristics of porous zirconium diboride (Z rB2), an Ultra-High-Temperature-Ceramic (UHTC) and a potential candidate for transpiration cooling of hypersonic vehicles. This is performed for both partially sintered material and fully densified material with cast features. The Darcy and Forchheimer permeability coefficients of these samples are determined using an ISO standard test rig. The outflow of the transpiring porous samples is investigated where no hypersonic cross-flow is involved using hot-wire anemometry and focused Schlieren visualisation. The velocity maps obtained from the hot-wire data show significant non-uniformities across the UHTC’s outflow region, both at low and high differential pressures. The focused Schlieren using carbon dioxide as the injected gas reveals unsteady structures at high differential pressures as the outflowing gas interacts with the surrounding air

Flow characterisation of transpiring porous media for hypersonic vehicles

This paper experimentally examines the internal and external flow characteristics of porous zirconium diboride (Z rB2), an Ultra-High-Temperature-Ceramic (UHTC) and a potential candidate for transpiration cooling of hypersonic vehicles. This is performed for both partially sintered material and fully densified material with cast features. The Darcy and Forchheimer permeability coefficients of these samples are determined using an ISO standard test rig. The outflow of the transpiring porous samples is investigated where no hypersonic cross-flow is involved using hot-wire anemometry and focused Schlieren visualisation. The velocity maps obtained from the hot-wire data show significant non-uniformities across the UHTC’s outflow region, both at low and high differential pressures. The focused Schlieren using carbon dioxide as the injected gas reveals unsteady structures at high differential pressures as the outflowing gas interacts with the surrounding air

Numerical Simulation of Transpiration Cooling in a Laminar Hypersonic Boundary Layer - Dataset

Two-dimensional simulations of transpiration cooling in a laminar, hypersonic boundary layer were performed using the thermochemical implicit nonequilibrium algorithm (TINA): a Navier–Stokes solver. Coolant concentration and heat flux results are compared to data obtained from laminar transpiration cooling experiments conducted in the Oxford High Density Tunnel employing a flat-plate geometry at Mach 7. TINA successfully predicts the mixing rate at the wall as a function of the streamwise direction for all blowing ratios. The simulations are more successful in predicting the mixing downstream of the injector as compared to the mixing on the injector: especially at low blowing ratios. A collapse of the thermal effectiveness values calculated from TINA simulation data is achieved, which agrees with laminar correlations within an absolute value of ±10%. It is shown that, when the concentration effectiveness is close to one at the injector, the temperature gradient becomes negative at locations immediately downstream of the injector, resulting in a negative heat flux. The acceleration of the coolant in the streamwise direction downstream promotes dissipation of energy, which results in a reduction in the temperature of the coolant, and thereby induces a negative temperature gradient close to the injector

Numerical simulation of transpiration cooling in a laminar hypersonic boundary layer

Two-dimensional simulations of transpiration cooling in a laminar, hypersonic boundary layer were performed using the thermochemical implicit nonequilibrium algorithm (TINA): a Navier–Stokes solver. Coolant concentration and heat flux results are compared to data obtained from laminar transpiration cooling experiments conducted in the Oxford High Density Tunnel employing a flat-plate geometry at Mach 7. TINA successfully predicts the mixing rate at the wall as a function of the streamwise direction for all blowing ratios. The simulations are more successful in predicting the mixing downstream of the injector as compared to the mixing on the injector: especially at low blowing ratios. A collapse of the thermal effectiveness values calculated from TINA simulation data is achieved, which agrees with laminar correlations within an absolute value of ±10%. It is shown that, when the concentration effectiveness is close to one at the injector, the temperature gradient becomes negative at locations immediately downstream of the injector, resulting in a negative heat flux. The acceleration of the coolant in the streamwise direction downstream promotes dissipation of energy, which results in a reduction in the temperature of the coolant, and thereby induces a negative temperature gradient close to the injector

Studying the film effectiveness of transpiration cooled walls using pressure sensitive paint

This paper presents the performance of pressure sensitive paint (PSP) for the direct investigation of a transpiration cooled surface. This technique allows the quantification of the pressure distribution on a porous surface with blowing. Additionally, it can be used to detect where the coolant is on the surface, thus measuring the transport of molecular oxygen to a transpiration cooled surface. For highly turbulent flows, it can also be used to evaluate the film effectiveness. A porous aluminium sample was anodised and dip coated in a PSP luminophore solution. It was fitted into a flat plate model and exposed to a Mach 5 cross-flow in the Oxford High Density Tunnel. Tests were conducted with no coolant injection, air injection and with nitrogen injection at increasing blowing ratios. The film effectiveness of the transpiration cooled surface was obtained for several conditions at Re = 15.5 - 31.5 10^6/m and F = 0.001 - 0.002. The film effectiveness increases as the Reynolds number decreases and the blowing ratio increases, which is in good qualitative agreement with the literature. Furthermore, it shows the same features as a velocity map of the outflow