# gst: phase transition of inertial self-propelled agents, a ‘inverse modeling’ approach.

AA << formulate and analyze a kinetic MFG (Mean-field Game) model for an interacting system of non-cooperative motile agents with inertial dynamics and finite-range interactions, where each agent is minimizing a biologically inspired cost function. >>️️

The << ‘inverse modelling’ approach is to stipulate that the collective behavior of a population of decision-making agents is a solution to a collective optimization or optimal control problem. (..) In a MFG system, the collective behavior is the result of each agent solving an optimal control problem that depends on its own state and control as well as the collective state. MFGs formulated in continuous state space and time are described by coupled set of forward-backward in time nonlinear partial differential equations (PDEs). >>

<< While standard kinetic or hydrodynamic equations used for modelling collective behavior are initial value problems (IVP or evolution PDEs), the MFG systems have a forward-backward in time structure, and hence consist of boundary value problem (BVP in time PDEs). >>

<< By analyzing the associated coupled forward-backward in time system of nonlinear Fokker-Planck and Hamilton-Jacobi-Bellman equations, (AA) obtain conditions for closed-loop linear stability of the spatially homogeneous MFG equilibrium that corresponds to an ordered state with non-zero mean speed. Using a combination of analysis and numerical simulations, (AA) show that when energetic cost of control is reduced below a critical value, this equilibrium loses stability, and the system transitions to a traveling wave solution. >>️

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Piyush Grover, Mandy Huo. Phase transition in a kinetic mean-field game model of inertial self-propelled agents. arXiv: 2407.18400v1 [math.OC]. Jul 25, 2024. 

https://arxiv.org/abs/2407.18400

Also: transition, wave, game, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, criticality, bifurcations, wave, games

# gst: apropos of 'filamentous' and 'fibrous' scenarios, criticality enhances the reinforcement of disordered networks by rigid inclusions.

<< The mechanical properties of biological materials are spatially heterogeneous. Typical tissues are made up of a spanning fibrous extracellular matrix in which various inclusions, such as living cells, are embedded. >>️

<< Recent work has shown that, in isolation, such networks exhibit unusual viscoelastic behavior indicative of an underlying mechanical phase transition controlled by network connectivity and strain. How this behavior is modified when inclusions are present is unclear. >>

AA << present a theoretical and computational study of the influence of rigid inclusions on the mechanics of disordered elastic networks near the connectivity-controlled central force rigidity transition. >>️

<< Combining scaling theory and coarse-grained simulations, (AA) predict and confirm an anomalously strong dependence of the composite stiffness on inclusion volume fraction, beyond that seen in ordinary composites. (..) this enhancement is a consequence of the interplay between inter-particle spacing and an emergent correlation length, leading to an effective finite-size scaling imposed by the presence of inclusions. >>

AA << show that this enhancement is a consequence of the interplay between inter-particle spacing and an emergent correlation length, leading to an effective finite-size scaling imposed by the presence of inclusions. >>️

AA << discuss potential experimental tests and implications for (their)  predictions in real systems. >>

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Jordan L. Shivers, Jingchen Feng, Fred C. MacKintosh. Criticality enhances the reinforcement of disordered networks by rigid inclusions. arXiv:  2407.19563v1 [cond-mat.soft]. Jul 28, 2024. 

https://arxiv.org/abs/2407.19563

Also: network, transition, disorder, elastic, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, transition, disorder, elasticity, rigidity, criticality, bifurcations

# gst: existence of hidden metastable states, bifurcations of inflating balloons and interacting hysterons.

AA << consider a system of connected rubber balloons that can be described by a Preisach model of noninteracting hysterons under pressure control but for which the hysterons become coupled under volume control. >>

<< Changes in the transition graphs turn out to be related to changes in the topology of the configuration space of the balloons, providing a particularly geometric view of how transition graphs can be designed, as well as additional information on the existence of hidden metastable states. This class of systems is more general than just balloons. >>️

Gentian Muhaxheri and Christian D. Santangelo. Bifurcations of inflating balloons and interacting hysterons. Phys. Rev. E 110, 024209. Aug 16, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.024209

Also: transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, balloons, bifurcations, hysteresis, hysterons, transition

# gst: apropos of coexistence of coherent and incoherent oscillators, chaotic chimera attractors in a triangular network.

<< A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains known as chimera states. >>️

<< In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically. >>

<< In this paper, (AA) study the full phase space dynamics of such three-population networks. (They) demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. >>

<< The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tristability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold. >>️

Seungjae Lee, Katharina Krischer. Chaotic chimera attractors in a triangular network of identical oscillators. Phys. Rev. E 107, 054205. May 8, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.054205

Also: chimera, chaos, three balls, in https://www.inkgmr.net/kwrds.html

Keywwords: gst, chimera, bifurcations, chaos, synchronization