scholarly journals Replicator–mutator dynamics of linguistic convergence and divergence

2020 ◽  
Vol 7 (11) ◽  
pp. 201682
Author(s):  
Henri Kauhanen
Keyword(s):  
Empirical Test ◽  
Evolutionary Game ◽  
Test Case ◽  
Identity Maintenance ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
Stable Equilibria ◽  
Linguistic Behaviour ◽  
Dynamic Equilibria ◽  
Special Case

People tend to align their use of language to the linguistic behaviour of their own ingroup and to simultaneously diverge from the language use of outgroups. This paper proposes to model this phenomenon of sociolinguistic identity maintenance as an evolutionary game in which individuals play the field and the dynamics are supplied by a multi-population extension of the replicator–mutator equation. Using linearization, the stabilities of all dynamic equilibria of the game in its fully symmetric two-population special case are found. The model is then applied to an empirical test case from adolescent sociolinguistic behaviour. It is found that the empirically attested population state corresponds to one of a number of stable equilibria of the game under an independently plausible value of a parameter controlling the rate of linguistic mutations. An asymmetric three-population extension of the game, explored with numerical solution methods, furthermore predicts to which specific equilibrium the system converges.

An Investigation Into the Compliance of SCARA Robots. Part II: Experimental and Numerical Validation

1988 ◽  
Vol 110 (1) ◽  
pp. 23-30 ◽  
Author(s):  
H. A. ElMaraghy ◽  
B. Johns
Keyword(s):  
Elastic Compliance ◽  
Servo Control ◽  
Compliance Matrix ◽  
End Effector ◽  
Prismatic Parts ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
Using Data ◽  
Assembly Performance ◽  
Robot Configurations

A model of inherent elastic compliance was developed for general position-controlled SCARA, with conventional joint feedback control, for both rotational and prismatic part insertion (Part I). The developed model was applied to the SKILAM and ADEPT I robots for validation. Experimental procedures and numerical solution methods are described. It was found that the ADEPT I robot employs a coupled control strategy between joints one and two which produces a constant, decoupled end effector compliance. The applicable compliance matrix, in this case, is presented and the experimental results are discussed. The model may be used to develop compliance maps that define the amount of end effector compliance, as a function of the joints compliance, as well as its variation for different robot configurations. This is illustrated using data for the SKILAM SCARA robot. Results are plotted and discussed. The most appropriate robot postures for assembly were found for both rotational and prismatic parts. The conditions necessary to achieve compliance or semicompliance centers with the SKILAM robot were examined. The results and methods demonstrated in these examples may be used to select appropriate robots for given applications. They can also guide robot designers in selecting joint servo-control gains to obtain the desired joints compliance ratio and improve assembly performance.

Nonequilibrium Continuum Traffic Flow Model with Frozen Sound Wave Speed

2003 ◽  
Vol 1852 (1) ◽  
pp. 183-192
Author(s):  
W. L. Jin ◽  
H. M. Zhang
Keyword(s):  
Traffic Flow ◽  
Sound Speed ◽  
Flow Model ◽  
Wave Model ◽  
Homogeneous System ◽  
Traffic Flow Model ◽  
Traffic Conditions ◽  
Numerical Solution Methods ◽  
Stable Conditions ◽  
Solution Methods

Results are presented from a recent study on a variation of a new non-equilibrium continuum traffic flow model in which traffic sound speed is constant. Hence this model is called the frozen-wave model. This model resembles the Payne–Whitham model but avoids the “back-traveling” of the latter. For this frozen-wave model, the Riemann problem is analyzed for its homogeneous system, two numerical solution methods are developed to solve it, and numerical simulations are carried out under both stable and unstable traffic conditions. These results show that under stable conditions, the model behaves similarly to the Payne–Whitham model. However, under unstable traffic conditions, it has nonphysical solutions or no solutions when a vacuum problem occurs. This study, on the one hand, provides a more complete picture of the properties of this frozen-wave model and reduces the risk of improper applications of it. On the other hand, it also highlights the need to adopt a density-dependent sound speed.

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