71,197 research outputs found
Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity
In this work we propose and analyze a numerical method for electrical
impedance tomography of recovering a piecewise constant conductivity from
boundary voltage measurements. It is based on standard Tikhonov regularization
with a Modica-Mortola penalty functional and adaptive mesh refinement using
suitable a posteriori error estimators of residual type that involve the state,
adjoint and variational inequality in the necessary optimality condition and a
separate marking strategy. We prove the convergence of the adaptive algorithm
in the following sense: the sequence of discrete solutions contains a
subsequence convergent to a solution of the continuous necessary optimality
system. Several numerical examples are presented to illustrate the convergence
behavior of the algorithm.Comment: 26 pages, 12 figure
Landscape and flux for quantifying global stability and dynamics of game theory
Game theory has been widely applied to many areas including economics,
biology and social sciences. However, it is still challenging to quantify the
global stability and global dynamics of the game theory. We developed a
landscape and flux framework to quantify the global stability and global
dynamics of the game theory. As an example, we investigated the models of
three-strategy games: a special replicator-mutator game, the repeated prison
dilemma model. In this model, one stable state, two stable states and limit
cycle can emerge under different parameters. The repeated Prisoner's Dilemma
system has Hopf bifurcation transitions from one stable state to limit cycle
state, and then to another one stable state or two stable states, or vice
versa. We explored the global stability of the repeated Prisoner's Dilemma
system and the kinetic paths between the basins of attractor. The paths are
irreversible due to the non-zero flux. One can explain the game for and
.Comment: 25 pages, 15 figure
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