28,670 research outputs found
Cooperation with both synergistic and local interactions can be worse than each alone
Cooperation is ubiquitous ranging from multicellular organisms to human
societies. Population structures indicating individuals' limited interaction
ranges are crucial to understand this issue. But it is still at large to what
extend multiple interactions involving nonlinearity in payoff play a role on
cooperation in structured populations. Here we show a rule, which determines
the emergence and stabilization of cooperation, under multiple discounted,
linear, and synergistic interactions. The rule is validated by simulations in
homogenous and heterogenous structured populations. We find that the more
neighbors there are the harder for cooperation to evolve for multiple
interactions with linearity and discounting. For synergistic scenario, however,
distinct from its pairwise counterpart, moderate number of neighbors can be the
worst, indicating that synergistic interactions work with strangers but not
with neighbors. Our results suggest that the combination of different factors
which promotes cooperation alone can be worse than that with every single
factor.Comment: 32 pages, 4 figure
Aspiration Dynamics of Multi-player Games in Finite Populations
Studying strategy update rules in the framework of evolutionary game theory,
one can differentiate between imitation processes and aspiration-driven
dynamics. In the former case, individuals imitate the strategy of a more
successful peer. In the latter case, individuals adjust their strategies based
on a comparison of their payoffs from the evolutionary game to a value they
aspire, called the level of aspiration. Unlike imitation processes of pairwise
comparison, aspiration-driven updates do not require additional information
about the strategic environment and can thus be interpreted as being more
spontaneous. Recent work has mainly focused on understanding how aspiration
dynamics alter the evolutionary outcome in structured populations. However, the
baseline case for understanding strategy selection is the well-mixed population
case, which is still lacking sufficient understanding. We explore how
aspiration-driven strategy-update dynamics under imperfect rationality
influence the average abundance of a strategy in multi-player evolutionary
games with two strategies. We analytically derive a condition under which a
strategy is more abundant than the other in the weak selection limiting case.
This approach has a long standing history in evolutionary game and is mostly
applied for its mathematical approachability. Hence, we also explore strong
selection numerically, which shows that our weak selection condition is a
robust predictor of the average abundance of a strategy. The condition turns
out to differ from that of a wide class of imitation dynamics, as long as the
game is not dyadic. Therefore a strategy favored under imitation dynamics can
be disfavored under aspiration dynamics. This does not require any population
structure thus highlights the intrinsic difference between imitation and
aspiration dynamics
RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure
models continue to play important roles in industrial flow simulations.
However, the commonly used linear eddy viscosity models are intrinsically
unable to handle flows with non-equilibrium turbulence. Reynolds stress models,
on the other hand, are plagued by their lack of robustness. Recent studies in
plane channel flows found that even substituting Reynolds stresses with errors
below 0.5% from direct numerical simulation (DNS) databases into RANS equations
leads to velocities with large errors (up to 35%). While such an observation
may have only marginal relevance to traditional Reynolds stress models, it is
disturbing for the recently emerging data-driven models that treat the Reynolds
stress as an explicit source term in the RANS equations, as it suggests that
the RANS equations with such models can be ill-conditioned. So far, a rigorous
analysis of the condition of such models is still lacking. As such, in this
work we propose a metric based on local condition number function for a priori
evaluation of the conditioning of the RANS equations. We further show that the
ill-conditioning cannot be explained by the global matrix condition number of
the discretized RANS equations. Comprehensive numerical tests are performed on
turbulent channel flows at various Reynolds numbers and additionally on two
complex flows, i.e., flow over periodic hills and flow in a square duct.
Results suggest that the proposed metric can adequately explain observations in
previous studies, i.e., deteriorated model conditioning with increasing
Reynolds number and better conditioning of the implicit treatment of Reynolds
stress compared to the explicit treatment. This metric can play critical roles
in the future development of data-driven turbulence models by enforcing the
conditioning as a requirement on these models.Comment: 35 pages, 18 figure
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