# gst: overcoming overly simplistic representations, chaos and regularity in an anisotropic soft squircle billiard.

<< A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. >>

<< Soft billiards are a generalization that includes a smooth boundary whose dynamics are governed by Hamiltonian equations and overcome overly simplistic representations. >>

AA << study the dynamical features of an anisotropic soft-wall squircle billiard. This curve is a geometric figure that seamlessly blends the angularity of a square with the smooth curves of a circle. (AA) characterize the billiard's emerging trajectories, exhibiting the onset of chaos and its alternation with regularity in the parameter space. (They) characterize the transition to chaos and the stabilization of the dynamics by revealing the nonlinearity of the parameters (squarness, ellipticity, and hardness) via the computation of Poincaré surfaces of section and the Lyapunov exponent across the parameter space. >>

AA << expect (Their) work to introduce a valuable tool to increase understanding of the onset of chaos in soft billiards. >>

A. González-Andrade, H. N. Núñez-Yépez, M. A. Bastarrachea-Magnani. Chaos and Regularity in an Anisotropic Soft Squircle Billiard. arXiv: 2504.20270v1 [nlin.CD]. Apr 28, 2025.

https://arxiv.org/abs/2504.20270

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

Keywords: gst, billiard, soft billiard, soft-wall squircle billiard, particles, smooth boundary,  specular collisions, transitions, chaos

# gst: apropos of critical transitions, a new approach to extreme events.

FIG. 1. Dynamics of excitable complex networks [coupling topologies: random (RN); small-world (SW); scale-free (SF); all-to-all (complete; CP)]. 

<< Unexpected and often irreversible shifts in the state or the dynamics of a complex system often accumulate in extreme events with likely disastrous impact on the system and its environment. Detection, understanding, and possible prediction of such critical transitions are thus of paramount importance across a variety of scientific fields. >>

<< The rather modest improvement achieved so far may be due previous research mostly concentrating on either particular subsystems, considered to be of vital importance for the generating mechanism of a critical transition, or on the system as a whole. These approaches only rarely take into account the intricate, time-dependent interrelatedness of subsystems that can essentially determine emerging behaviors underlying critical transitions. >> 

AA << uncover subsystems, network vertices, and the interrelatedness of certain subsystems, network edges, as tipping elements in a networked dynamical system, forming a time-evolving tipping subnetwork. (They)  demonstrate the existence of tipping subnetworks in excitable complex networks and in human epileptic brains. These systems can repeatedly undergo critical transitions that result in extreme events. >>

AA << findings reveal that tipping subnetworks encapsulate key properties of mechanisms involved in critical transitions. >>

Timo Bröhl, Klaus Lehnertz. Emergence of a tipping subnetwork during a critical transition in networked systems: A new avenue to extreme events. Phys. Rev. Research 7, 023109. May 1, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023109

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

Keywords: gst, networks, excitable complex networks, network edges, network vertices, subnetwork, tipping subnetworks, small-worlds, unexpected shifts, transitions, critical transition, extreme events, interrelatedness, time-dependent interrelatedness.

# gst: emergent oscillations and chaos in noncompliant microfluidic networks.

<< Incompressible fluids in microfluidic networks with nonrigid channels can exhibit flow rate oscillations analogous to electric current oscillations in RLC (resistor, inductor, capacitor) circuits. This is due to the elastic deformation of channel walls that can store and release fluid, as electric capacitors can store and release electric charges. This property is quantified through the compliance of the system, defined as the volume change relative to the pressure change. >>

<< In systems with rigid walls and incompressible fluid, compliance vanishes, and no oscillations can occur through this mechanism. >>

Here, AA << show that not only oscillations but also chaos can emerge in the flow-rate dynamics of noncompliant microfluidic networks with incompressible fluid. Notably, these dynamics emerge spontaneously, even under time-independent driving pressures. The underlying mechanism is governed by the effect of fluid inertia, which becomes relevant at moderate Reynolds numbers observed in microfluidic systems exhibiting complex flow patterns. >>

<< The results are established using a combination of direct numerical simulations and a reduced model derived from modal analysis. This approach enables (AA) to determine the onset of oscillations, the associated bifurcations, the oscillation frequencies and amplitudes, and their dependence on the driving pressures. >>

Yanxuan Shao, Jean-Regis Angilella, Adilson E. Motter. Emergent oscillations and chaos in noncompliant microfluidic networks. Phys. Rev. Fluids 10, 054401. May 1, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.054401

arXiv: 2505.00068v1 [physics.flu-dyn]. 

https://arxiv.org/abs/2505.00068

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

Keywords: gst, networks, microfluidic networks, noncompliant networks with incompressible fluid, fluid inertia, 

driving pressures, elasticity, chaos.

# gst: apropos of adaptation of simple organisms to changing environments, self-organization and memory in a disordered entity to random driving.

AA << consider self-organization and memory formation in a mesoscopic model of an amorphous solid subject to a protocol of random shear confined to a strain range ±𝜖max. (They) develop proper readout protocols to show that the response of the driven system self-organizes to retain a memory of the strain range, which can be subsequently retrieved. >>

AA << findings generalize previous results obtained upon oscillatory driving and suggest that self-organization and memory formation of disordered materials can emerge under more general conditions, such as a disordered system interacting with its fluctuating environment. Self-organization results in a correlation between the dynamics of the system and its environment, providing thereby an elementary mechanism for sensing. >>

AA << conclude by discussing (Their)  results and their potential relevance for the adaptation of simple organisms lacking a brain to changing environments. >>

Muhittin Mungan, Dheeraj Kumar, et al. Self-Organization and Memory in a Disordered Solid Subject to Random Driving. Phys. Rev. Lett. 134, 178203. April 30, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.178203

arXiv: 2409.17096v2 [cond-mat.soft]. 

https://arxiv.org/abs/2409.17096

Also: disorder & fluctuations, 

self-assembly, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, fluctuations, self-assembly, self-organization, transitions

# gst: inverse design of Kirigami; contracted shapes, deployed shapes, internal trajectories of rotating units.

<< Kirigami metamaterials have enabled a plethora of morphing patterns across art and engineering. However, the inverse design of kirigami for complex shapes remains a puzzle that so far cannot be solved without relying on complex numerical methods. >>

Here, AA << present a purely geometric design method to overcome the reliance on sophisticated numerical algorithms and showcase how to leverage it for three distinct types of morphing targets, i.e., the contracted shape, the deployed shape, and the internal trajectories of the rotating units in kirigami specimens. >>

AA << results unveil the fundamental relations between the kirigami deformation and the shape of its rotating units and enable us to establish the underpinning physics through theoretical investigations validated via numerical simulations. >>

Chuan Qiao, Shijun Chen, et al. Inverse Design of Kirigami through Shape Programming of Rotating Units. Phys. Rev. Lett. 134, 176103. May 2, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.176103

Also: kirigami, origami, metamorphosis,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, kirigami, origami, metamorphosis

# gst: like fireflies or neurons, dynamics of pulsating swarmalators on a ring.

AA << study a simple one-dimensional model of swarmalators, a generalization of phase oscillators that swarm around in space as well as synchronize internal oscillations in time. Previous studies of the model focused on Kuramoto-type couplings, where the phase interactions are governed by phase differences. >>

 Here AA << consider Winfree-type coupling, where the interactions are multiplicative, determined by the product of a phase response function  and phase pulse function . This more general interaction (from which the Kuramoto phase differences emerge after averaging) produces rich physics: six long-term modes of organization are found, which we characterize numerically and analytically. >>

Samali Ghosh, Kevin O'Keeffe, et al. Dynamics of pulsating swarmalators on a ring. arXiv: 2504.14912v1 [nlin.AO]. Apr 21, 2025. 

https://arxiv.org/abs/2504.14912

Also: swarm, swarmalators, instability, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swarm, swarmalators, instability

# gst: transitions of breakup regimes for viscous droplets in airflow.

In this AA study, << the transitions of breakup regimes for viscous droplets are investigated experimentally using high-speed imaging taken from a side view and a 45 view. Based on the morphology change in the middle of the droplet, the breakup regimes are classified into no-breakup, bag breakup, bag-stamen, low-order multimode, high-order multimode, and shear-stripping breakup. The droplet morphologies in different regimes and the corresponding transitions are discussed in detail. >>

<< The droplet viscosity dissipates the kinetic energy transferred by the airflow during the initial droplet flattening, and affects the development of the Rayleigh-Taylor instability wave after the flattening. Through the analysis of the droplet deformation and the Rayleigh-Taylor instability with the droplet viscosity taken into account, the transition conditions of different regimes are obtained in a regime map. By further considering the relative velocity loss between the droplet and the airflow, the ranges of the dual-bag breakup in the low-order multimode regime and the droplet retraction in the bag-stamen regime are determined. >>

Zhikun Xu, Tianyou Wang, Zhizhao Che. Transitions of breakup regimes for viscous droplets in airflow. arXiv: 2504.14149v1 [physics.flu-dyn]. Apr 19, 2025.

https://arxiv.org/abs/2504.14149

Also: drop, droplet, droploid, transition, instability, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drops, droplets, droploids, viscous droplets, droplet breakup, transitions, instability, waves