# gst: apropos of transitions, towards a theory for the formation of chimera patterns in complex networks

This AA work << formalizes a systematic method by evoking pattern formation theory to explain the emergence of chimera states in complex networks. >>

They << show that the randomness of network topology, as reflected in the localization of the graph Laplacian eigenvectors, determines the emergence of chimera patterns, underscoring the critical role of network structure. In particular, this approach explains how amplitude and phase chimeras arise separately and explores whether phase chimeras can be chaotic or not. (AA) findings suggest that chimeras result from the interplay between local and global dynamics at different time scales. >>

Malbor Asllani, Alex Arenas. Towards a Theory for the Formation of Chimera Patterns in Complex Networks. arXiv: 2412.05504v1 [nlin.AO]. Dec 7, 2024.

https://arxiv.org/abs/2412.05504

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

Keywords: gst, chimera, network, transition

# gst: turbulence in viscous binary fluid mixtures induced by interfacial fluctuations.

AA << demonstrate the existence of interface-induced turbulence, an emergent nonequilibrium statistically steady state with spatiotemporal chaos, which is induced by interfacial fluctuations in low-Reynolds-number binary-fluid mixtures. >>️

<< Furthermore (they) demonstrate diffusive behavior at long times, a hallmark of strong mixing in turbulent flows. >>️

Nadia Bihari Padhan, Dario Vincenzi, Rahul Pandit. Interface-induced turbulence in viscous binary fluid mixtures. Phys. Rev. Fluids 9, L122401. Dec 3, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.L122401

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

Keywords: gst, fluctuations, turbulence, transition 

# gst: apropos of puddles, how to design and stabilize a Leidenfrost puddle

<< Leidenfrost puddles exhibit erratic bubble bursts that release vapor trapped beneath the liquid, becoming amorphous and unstable. (AA) report a method to stabilize and design a Leidenfrost puddle. >>

<< When a thin hydrophilic layer with a suitable design is placed over the liquid, the puddle adopts the layer shape due to adhesive forces and becomes stable. (AA) show a variety of puddle designs with the required layer dimensions to avoid vapor accumulation, as well as wetting and buoyancy conditions. >>

<< With the layer, the puddle evaporation rate increases significantly and can be modified by varying the layer dimensions. Finally, an illustrative use of this method in a cooling process is presented. >>️

F. Pacheco-Vázquez, M. Aguilar-González, L. Victoria-García. Designing Leidenfrost Puddles. Phys. Rev. Lett. 133, 234001. Dec 4, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.234001 

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

Keywords: gst, drops, bubbles, instability, transition

# gst: anomalous oscillation modes of (superfluid) pendant droplets; horizontal translation on a flat surface, bouncing off at the corner and vertical oscillations at the edge.

<< Droplets should exhibit various dynamical phenomena when adhered to a surface; not all of them are realized in classical fluids. Visualization of superfluid  4^He (helium-4) pendant droplets revealed that the droplets were horizontally translated on a flat surface, bouncing off at the corner, known as the Noether mode that reflects the translation symmetry. >>️

<< The droplets exhibited another mode in vertical oscillations with high amplitude that included oscillation of the droplet edge. The oscillation period remained constant even as the droplets grew, exhibiting an anomalously weak size dependence. The high mobility of the droplet edges owing to the superfluidity was a crucial factor for the appearance of these anomalous modes. >>️

Keita Onodera, Ryuma Nagatomo, et al. Anomalous Oscillation Modes of Superfluid Pendant Droplets. Phys. Rev. Lett. 133, 216001. Nov 19, 2024.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.216001

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

Keywords: gst, drop, droplet, droploid, transition

# gst: when a pseudo pyramid cyclically flips; (lab) icebergs melt down and flip out

AA << study laboratory-scale icebergs that freely float and melt, where direct visualizations show interesting and interconnected changes in the shape of the ice, its posture, and the flows of the surrounding water. >>️

<< Ice in nature is dynamic at all scales, from glacial sheets that deform and flow to icebergs that melt down and capsize. For the latter, much of the ice and much of the action is unseen beneath the surface. >>️

<< Here (AA) study laboratory-scale icebergs that freely float and melt, where direct visualizations show interesting and interconnected changes in the shape of the ice, its posture, and the flows of the surrounding water. >>️

Bobae Johnson, Zihan Zhang, et al. Lab icebergs melt down and flip out. Phys. Rev. Fluids 9, 110510. Nov 22, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.110510

Bobae Johnson, Steven Zhang, et al. P0011: Lab icebergs melt down and flip out. 76th Annual Meeting of the APS Division of Fluid Dynamics. Nov 19-21, 2023. 

https://gfm.aps.org/meetings/dfd-2023/64fb5761199e4c7f75b63ef7

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

Keywords: gst, transition

# gst: protected chaos in a topological lattice.

<< The erratic nature of chaotic behavior is thought to erode the stability of periodic behavior, including topological oscillations. However, (AA) discover that in the presence of chaos, non-trivial topology not only endures but also provides robust protection to chaotic dynamics within a topological lattice hosting non-linear oscillators. >>

<< Despite the difficulty in defining topological invariants in non-linear settings, non-trivial topological robustness still persists in the parametric state of chaotic boundary oscillations. (AA) demonstrate this interplay between chaos and topology by incorporating chaotic Chua's circuits into a topological Su-Schrieffer-Heeger (SSH) circuit. >>

<< By extrapolating from the linear limit to deep into the non-linear regime, (AA) find that distinctive correlations in the bulk and edge scroll dynamics effectively capture the topological origin of the protected chaos. (Their)  findings suggest that topologically protected chaos can be robustly achieved across a broad spectrum of periodically-driven systems, thereby offering new avenues for the design of resilient and adaptable non-linear networks. >>️

Haydar Sahin, Hakan Akgün, et al. Protected chaos in a topological lattice. arXiv: 2411.07522v1 [cond-mat.mes-hall]. Nov 12, 2024.

https://arxiv.org/abs/2411.07522

Also: chaos, random, instability, transition, network, ai (artificial intell), in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, random,  instability, transition, network, AI, Artificial Intelligence

# gst: singular bifurcations, an approach

<< Bifurcation analysis is traditionally based on the assumption of a regular perturbative expansion, close to the bifurcation point, in terms of a variable describing the passage of a system from one state to another. However, it is shown that a regular expansion is not the rule due to the existence of hidden singularities in many models, paving the way to a new paradigm in nonlinear science, that of singular bifurcations. The theory is first illustrated on an example borrowed from the field of active matter (phoretic microswimers), showing a singular bifurcation. >>

AA << then present a universal theory on how to handle and regularize these bifurcations, bringing to light a novel facet of nonlinear sciences that has long been overlooked. >>️

Alexander Farutin, Chaouqi Misbah. Singular bifurcations and regularization theory. Phys. Rev. E 109, 064218. Jun 27, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064218

Alexander Farutin, Chaouqi Misbah. Singular Bifurcations : a Regularization Theory. arXiv: 2112.12094v2 [cond-mat.soft]. Jan 6, 2022. 

https://arxiv.org/abs/2112.12094 

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

Keywords: gst, transition, singularity, bifurcation

# gst: pulse-to-crack transition, unsteady slip pulses under spatially-varying prestress scenarios.

AA << study the effects of a spatially-varying prestress τb(x) on 2D slip pulses, initially generated under a uniform τb along a rate-and-state friction fault. (They) consider periodic and constant-gradient prestress τb(x) around the reference uniform τb. For a periodic τb(x), pulses either sustain and form quasi-limit cycles in the L−c plane or decay predominantly monotonically along the L(c) line, depending on the instability index of the initial pulse and the properties of the periodic τb(x).  >>️

<< For a constant-gradient τb(x), expanding/decaying pulses closely follow the L(c) line, with systematic shifts determined by the sign and magnitude of the gradient. (They) also find that a spatially-varying τb(x) can revert the expanding/decaying nature of the initial reference pulse.  >>

<< Finally, (AA) show that a constant-gradient τb(x), of sufficient magnitude and specific sign, can lead to the nucleation of a back-propagating rupture at the healing tail of the initial pulse, generating a bilateral crack-like rupture. This pulse-to-crack transition, along with the above-described effects, demonstrate that rich rupture dynamics merge from a simple, nonuniform prestress. >>️️

Anna Pomyalov, Eran Bouchbinder. Unsteady slip pulses under spatially-varying prestress. arXiv: 2407.21539v1 [cond-mat.mtrl-sci]. Jul 31, 2024.

https://arxiv.org/abs/2407.21539

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

Keywords: gst, transition, instability, crack 

# gst: underdamped and overdamped scenarios of a one-dimensional inertial run-and-tumble particle

AA << study the nonequilibrium stationary state of a one-dimensional inertial run-and-tumble particle  trapped in a harmonic potential. (AA) find that the presence of inertia leads to two distinct dynamical scenarios, namely, overdamped and underdamped, characterized by the relative strength of the viscous and the trap timescales. >>

️

<< in the underdamped regime, both the position and velocity undergo transitions from a novel multipeaked structure in the strongly active limit to a single-peaked Gaussian-like distribution in the passive limit. On the other hand, in the overdamped scenario, the position distribution shows a transition from a U shape to a dome shape, as activity is decreased. Interestingly, the velocity distribution in the overdamped scenario shows two transitions—from a single-peaked shape with an algebraic divergence at the origin in the strongly active regime to a double-peaked one in the moderately active regime to a dome-shaped one in the passive regime. >>️

Debraj Dutta, Anupam Kundu, et al. Harmonically trapped inertial run-and-tumble particle in one dimension. Phys. Rev. E 110, 044107. Oct 4, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.044107

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

Keywords: gst, particle, transition 

# gst: isles of regularity (depending on the initial setup) in a sea of chaos amid the gravitational three-body problem.

AA << study probes the presence of regular (i.e. non-chaotic) trajectories within the 3BP (three-body problem) and assesses their impact on statistical escape theories. >>

AA << analysis reveals that regular trajectories occupy a significant fraction of the phase space, ranging from 28% to 84% depending on the initial setup, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. >>

Alessandro Alberto Trani, Nathan W.C. Leigh, et al. Isles of regularity in a sea of chaos amid the gravitational three-body problem. A&A, 689, A24, Jun 25, 2024.

https://www.aanda.org/articles/aa/full_html/2024/09/aa49862-24/aa49862-24.html

"Islands" of Regularity Discovered in the Famously Chaotic Three-Body Problem. University of Copenhagen. Oct 11, 2024.

https://science.ku.dk/english/press/news/2024/islands-of-regularity-discovered-in-the-famously-chaotic-three-body-problem/

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

Keywords: gst, three balls, escape, chaos, transition 

# gst: apropos of fluctuations, an unconventional approach to (fuzzy) morphogenesis

AA << propose an unconventional mechanism where stochastic fluctuations drive the emergence of morphological patterns. >>️

In this approach << the inherent fluctuations determine the nature of the dynamics and are not incidental noise in the background of the otherwise deterministic dynamics. Instead, they play an important role as a driving force that defines the attributes of the pattern formation dynamics and the nature of the transition itself.  >>️

Oded Agam and Erez Braun. Fluctuation-driven morphological patterning: An unconventional approach to morphogenesis. Phys. Rev. Research 6, 043027. Oct 10, 2024.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043027

Also: disorder & fluctuations, self-assembly, metamorphosis, transition, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, fluctuations,  self-assembly, metamorphosis, transition, noise

# gst: extreme events in two-coupled chaotic oscillators.

This AA study << focuses on the emergence of extreme events in a system of diffusively and bidirectionally two coupled Rössler oscillators and unraveling the mechanism behind the genesis of extreme events. (AA) find the appearance of extreme events in three different observables: average velocity, synchronization error, and one transverse directional variable to the synchronization manifold. >>

<< The emergence of extreme events in average velocity variables happens due to the occasional in-phase synchronization. The on-off intermittency plays for the crucial role in the genesis of extreme events in the synchronization error dynamics and in the transverse directional variable to the synchronization manifold. The bubble transition of the chaotic attractor due to the on-off intermittency is illustrated for the transverse directional variable. >>

S. Sudharsan, Tapas Kumar Pal, et al. Extreme events in two-coupled chaotic oscillators. arXiv: 2409.15855v1 [nlin.CD]. Sep 24, 2024. 

https://arxiv.org/abs/2409.15855

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

Keywords: gst, transition, bubble transition, extreme events

# gst: dynamics of pulsating spheres orbiting black holes.

AA << study the chaotic dynamics of spinless extended bodies in a wide class of spherically symmetric spacetimes, which encompasses black-hole scenarios in many modified theories of gravity. (They) show that a spherically symmetric pulsating ball may have chaotic motion in this class of spacetimes. >>

AA << use Melnikov's method to show the presence of homoclinic intersections, which imply chaotic behavior, as a consequence of (their)  assumption that the test body has an oscillating radius. >>

Fernanda de F. Rodrigues, Ricardo A. Mosna, Ronaldo S. S. Vieira. Chaotic dynamics of pulsating spheres orbiting black holes. arXiv: 2409.14667v1 [gr-qc]. Sep 23, 2024.

https://arxiv.org/abs/2409.14667

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

Keywords: gst, black hole, homoclinic orbit, chaos, transition

# gst: apropos of intermittent switchings, presence of chaotic saddles in fluid turbulence.

<< Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a low-dimensional system accompanied by the stability change of a fixed point or a periodic orbit in that the intermittency of a high-dimensional system tends to appear in a wide range of parameters. >>️

Here AA << demonstrate the presence of chaotic saddles underlying intermittency in fluid turbulence and phase synchronization. Furthermore, (they) confirm that chaotic saddles persist for a wide range of parameters. Also, a kind of phase synchronization turns out to occur in the turbulent model. >>️

Hibiki Kato, Miki U Kobayashi, et al. A laminar chaotic saddle within a turbulent attractor. arXiv: 2409.08870v1 [nlin.CD]. Sep 13, 2024. 

https://arxiv.org/abs/2409.08870

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

Keywords: gst, transition, turbulence, intermittency, chaos

# gst: simultaneous presence of attraction and repulsion in quantum self-sustained oscillators

AA << study the emergent dynamics of quantum self-sustained oscillators induced by the simultaneous presence of attraction and repulsion in the coupling path. >>

They << discover an interesting symmetry-breaking transition from quantum limit cycle oscillation to a quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from a quantum homogeneous state to an inhomogeneous steady state. >>

<< Remarkably, (they) find the generation of entanglement associated with the symmetry-breaking transition that has no analog in the classical domain. >>

Bulti Paul, Biswabibek Bandyopadhyay, Tanmoy Banerjee. Attractive-repulsive interaction in coupled quantum oscillators. Phys. Rev. E 110, 034210. Sept 19, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.034210

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

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

# gst: a body of revolution with a cat’s toy mechanism.

AA << introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. >>

️

They << prove that (this system can be) integrable if the generalized momentum M is vertical (i.e. parallel to γ) and exhibit numerical evidence that it is chaotic otherwise. >>️

M. Costa Villegas, L.C. García-Naranjo. Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane. arXiv: 2409.08072v1 [math-ph]. Sep 12, 2024. 

https://arxiv.org/abs/2409.08072

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

Keywords: gst, transition, chaos

# gst: vortex structures under dimples and scars in turbulent free-surface flows

<< Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling 'boils', near-circular 'dimples' and elongated 'scars', easily identifiable by eye, e.g., in riverine flows. >>️

AA << explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. >>️

<< The analysis shows that the likelihood of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers in a near-Gaussian manner, influenced by the dimple's size and the bulk turbulence. When expressed as a function of depth over the Taylor microscale λT, this probability is independent of Reynolds and Weber number. >>️

<< Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, at a depth of approximately λT/4. Distributions of vortical orientation also show a clear pattern: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. >>️

AA << findings suggest that scars can be defined as imprints of horizontal vortices approximately a quarter of the Taylor microscale beneath the surface, analogous to how dimples can be defined as imprints of surface-attached vertical vortex tubes. >>

Jørgen R. Aarnes, Omer Babiker, et al. Vortex structures under dimples and scars in turbulent free-surface flows. arXiv: 2409.05409v1 [physics.flu-dyn]. 

9 Sep 2024.

https://arxiv.org/abs/2409.05409

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

Keywords: gst, vortex, turbulence, waves, bubble, drop, transition

# 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: 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