# 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: attractive-repulsive interaction in coupled qu-oscillators, when a symmetry-breaking state could be a prominent state.

AA << have explored the role of attractive repulsive coupling in shaping the collective behavior of coupled oscillators in the quantum domain. >>

<< A direct simulation (..) showed a symmetry breaking transition from quantum limit cycle to quantum oscillation death state with increasing coupling strength. >>️

<< This is in contrast to the quantum symmetry-breaking transitions reported earlier where inhomogeneity emerges from the homogeneous steady state. >>️

<< The phenomenon is general as it occurs at both weak and deep quantum regime. Specially, in the deep quantum regime where quantum noise is strong, yet it can not wash out the inhomogeneous state indicating that the symmetry-breaking state is indeed a prominent state. >>️️

Bulti Paul, Biswabibek Bandyopadhyay, Tanmoy Banerjee. Attractive-repulsive interaction in coupled quantum oscillators. arXiv: 2408.12972v1 [quant-ph]. Aug 23, 2024.

https://arxiv.org/abs/2408.12972

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

Keywords: gst, transition, symmetry-breaking transition, noise, attractive-repulsive interaction, coupled qu-oscillator

# gst: symmetry breaking and️ ️hyperuniformity in low-dimensional systems caused by inhomogeneous oscillatory driving forces.

<< The driving forces of chiral active particles and deformations of cells are often modeled by spatially inhomogeneous but temporally periodic driving forces. Such inhomogeneous oscillatory driving forces have only recently been proposed in the context of active matter, and their effects on the systems are not yet fully understood. >>️

AA << theoretically study the impact of spatially inhomogeneous oscillatory driving forces on continuous symmetry breaking. (They) first analyze the linear model for the soft modes in the ordered phase to derive the lower critical dimension of the model, and then analyze the spherical model to investigate more detailed phase behaviors.  >>

<< Interestingly, (their) analysis reveals that symmetry breaking occurs even in one and two dimensions, where the Hohenberg-Mermin-Wagner theorem prohibits continuous symmetry breaking in equilibrium. Furthermore, fluctuations of conserved quantities, such as density, are anomalously suppressed in the long-wavelength, i.e., show hyperuniformity. >>️️

Harukuni Ikeda, Yuta Kuroda. Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces. Phys. Rev. E 110, 024140. Aug 29, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.024140

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

Keywords: gst, transition

# 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: dynamics of small droplets in turbulent multiphase flows

AA << show unambiguously that the formation of small droplets is governed by the internal dynamics which occurs during the breakup of large drops and that the high vorticity and the extreme dissipation associated to these events are the consequence and not the cause of the breakup. >>️

M. Crialesi-Esposito, G. Boffetta, L. Brandt, et al. How small droplets form in turbulent multiphase flows. Phys. Rev. Fluids 9, L072301. Jul 29, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.L072301

Also: drop, bubble, transition, turbulence, intermittency, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid,  bubble, transition, turbulence, intermittency

# gst: distance to criticality in unknown noise

<< real-world systems are often corrupted by unknown levels of noise that can distort (..) temporal signatures. Here (AA) aim to develop noise-robust indicators of the distance to criticality (DTC) for systems affected by dynamical noise in two cases: when the noise amplitude is either fixed or is unknown and variable across recordings. >>️

<< in the variable-noise setting, where (..) conventional indicators perform poorly, (AA) highlight new types of high-performing time-series features and show that their success is accomplished by capturing the shape of the invariant density (which depends on both the DTC and the noise amplitude) relative to the spread of fast fluctuations (which depends on the noise amplitude). (AA) introduce a new high-performing time-series statistic, the rescaled autodensity (RAD). >>️

Brendan Harris, Leonardo L. Gollo, Ben D. Fulcher. Tracking the Distance to Criticality in Systems with Unknown Noise. Phys. Rev. X 14, 031021. Aug 8, 2024.

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.031021

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

Keywords: gst, criticality, bifurcation, noise, transition

# 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