# gst: critical crack length during fracture.

AA << established an inverse correlation between the strength of the material and the cracks which grow inside it—both the maximum crack and the one that sets in instability within the system, defined to be the critical crack. >>

AA << found that the maximum and the critical crack often differ from each other unless the disorder strength is extremely low. A phase diagram on the plane of disorder vs system size demarcates between the regions where the largest crack is the most vulnerable one and where they differ from each other but still show moderate correlation. >>️

Viswakannan R.K., Subhadeep Roy. Critical crack length during fracture. Phys. Rev. E 110, 024134. Aug 26, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.024134

Also: crack, instability, fluctuations, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, crack, instability, fluctuations, noise, criticality

# 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. >>️

️

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. >>

️

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: 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: near a critical point, switching between exploitation and exploration, to approach life with Lévy's (chaotic) walk

<< Lévy walks are common biological movements. However, the functional advantages of Lévy walks emerging near a critical point are poorly understood. >>

AA << showed that there could be functional advantages associated with Lévy walks emerging near a critical point, including a large dynamic range to stimuli and highly flexible switching between exploitation and exploration. >>

Masato S. Abe. Functional advantages of Lévy walks emerging near a critical point. PNAS.  doi: 10.1073/ pnas.2001548117.  Sep 14, 2020.

https://www.pnas.org/content/early/2020/09/11/2001548117

Chaotic 'Lévy walks' are a good strategy for animals. Riken. Sep 17, 2020.

https://phys.org/news/2020-09-chaotic-lvy-good-strategy-animals.html   

Also

Lévy flight hypothesis, not only for predation ...  Nov 22, 2015.

https://flashontrack.blogspot.com/2015/11/s-gst-levy-flight-hypothesis-not-only.html

keyword 'Lévy' in FonT

https://flashontrack.blogspot.com/search?q=L%C3%A9vy&m=1

# gst: critical points seem to act behind the complex behavior of collectives.

<< Current experiments support the controversial hypothesis that a well-known concept in physics—a critical point—is behind the striking behavior of collective animal systems. >>

AA << showed that light-controlled microswimming particles can be made to organize into collective states such as swarms and swirls. By studying the particles fluctuating between these states, they provide evidence for critical behavior—and support for a physical principle underlying the complex behavior of collectives.>>

<< What we observed is that the system can make sudden transitions from one state to the other, which demonstrates the flexibility needed to react to an external perturbation like a predator, (..) and provides clear evidence for a critical behavior. >> Clemens Bechinger

<< Through very simple interactions, they have shown that you can tune a physical system to a collective state - criticality - of balance between order and disorder. >> Iain Couzin

Physics principle explains order and disorder of swarms. University of Konstanz. Jun 11, 2020.

https://phys.org/news/2020-06-physics-principle-disorder-swarms.html

Bauerle T., Loffler R.C., Bechinger C. Formation of stable and responsive collective states in suspensions of active colloids. Nat Commun 11, 2547. doi: 10.1038/ s41467-020-16161-4. May 21, 2020.

https://www.nature.com/articles/s41467-020-16161-4

Also 

keyword 'self-assembly' in FonT

https://flashontrack.blogspot.com/search?q=self-assembly