# 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

# 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: 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

# gst: networks of pendula with diffusive interactions, chaotic regime seems to emerge at low energies.

AA << study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian; as such, the energy is conserved. >>️

<< The behaviour observed showcases a mechanism for the appearance of chaotic oscillations in conservative systems. For Hamiltonians with two degrees of freedom, it has been shown how chaos can emerge near a saddle-centre equilibrium possessing a homoclinic orbit. (AA) have seen that higher-dimensional systems having mixed equilibria, i.e., generalisations of a saddle-center where the eigenvalues are only imaginary and reals, also show chaotic behaviour close to those points.  >>️

AA << complement the analysis with some numerical simulations showing the interplay between bifurcations of the origin and transitions to chaos of nearby orbits. A key feature is that the observed chaotic regime emerges at low energies. >>

️

Riccardo Bonetto, Hildeberto Jardón-Kojakhmetov, Christian Kuehn. Networks of Pendula with Diffusive Interactions. arXiv: 2408.02352v1 [math.DS]. Aug 5, 2024.

https://arxiv.org/abs/2408.02352

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

Keywords: gst, pendulum, network, transition, chaos, bifurcation

# gst: emergent chirality in active rotation even with spontaneous chiral symmetry breaking.

<< Collective cell dynamics play a crucial role in many developmental and physiological contexts. While two-dimensional (2D) cell migration has been widely studied, how three-dimensional (3D) geometry and topology interplay with collective cell behavior to determine dynamics and functions remains an open question. >>️

<< Using murine pancreas-derived organoids as a model system, (AA) find that epithelial spheres exhibit persistent rotation, rotational axis drift, and rotation arrest. Using a 3D vertex model, (they) demonstrate how the combined action of traction force and polarity alignment can account for these distinct rotational dynamics near a solid to flow transition. Furthermore, (their) analysis shows that the spherical tissue rotates as an active solid occasionally switching to a flowing state and exhibits spontaneous chiral symmetry breaking. >>️

Tzer Han Tan, Aboutaleb Amiri, et al. Emergent chirality in active solid rotation of pancreas spheres. PRX Life 2, 033006. Aug 8, 2024.

https://journals.aps.org/prxlife/abstract/10.1103/PRXLife.2.033006

AA << say their work shows how symmetry-breaking processes in living active matter can be induced by the interplay of geometry, topology, and collective dynamics. >>️

Charles Day. Emergent Chirality in Active Rotation. Physics 17, s102. Aug 8, 2024. 

https://physics.aps.org/synopsis-for/10.1103/PRXLife.2.033006 

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

Keywords: gst, transition, chiral, chiral symmetry breaking