# gst: discontinuous transitions to active nematic turbulence.

<< Active fluids exhibit chaotic flows at low Reynolds number known as active turbulence. Whereas the statistical properties of the chaotic flows are increasingly well understood, the nature of the transition from laminar to turbulent flows as activity increases remains unclear. Here, through simulations of a minimal model of unbounded active nematics, (AA) find that the transition to active turbulence is discontinuous. (They) show that the transition features a jump in the mean-squared velocity, as well as bistability and hysteresis between laminar and chaotic flows. >>

<< From distributions of finite-time Lyapunov exponents, (AA) identify the transition at a value A∗≈4900 of the dimensionless activity number. Below the transition to chaos, (They) find subcritical bifurcations that feature bistability of different laminar patterns. These bifurcations give rise to oscillations and to chaotic transients, which become very long close to the transition to turbulence. Overall, (Their) findings contrast with the continuous transition to turbulence in channel confinement, where turbulent puffs emerge within a laminar background. >>

AA << propose that, without confinement, the long-range hydrodynamic interactions of Stokes flow suppress the spatial coexistence of different flow states, and thus render the transition discontinuous. >>️

Malcolm Hillebrand, Ricard Alert. Discontinuous Transition to Active Nematic Turbulence. arXiv: 2501.06085v1 [cond-mat.soft]. Jan 10, 2025.

https://arxiv.org/abs/2501.06085

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

Keywords: gst, chaos, transition, turbulence, jumps, active nematics

# gst: quadrupolar stress drives collapse of nematic order on frictional substrates.

<< The field of active nematics has traditionally employed descriptions based on dipolar activity, with interactions that align along a single axis. However, it has been theoretically predicted that interactions with a substrate, prevalent in most biological systems, would require novel forms of activity, such as quadrupolar activity, that are governed by hydrodynamic screening. >>

<< Here, by combining experiments and numerical simulations, (AA) show that upon light-induced solidification of the underlying medium, microtubule-kinesin mixtures undergo a transformation that leads to a biphasic active suspension. Using an active lyotropic model, (They) prove that the transition is governed by screening effects that alter the dominant form of active stress. Specifically, the combined effect of friction and quadrupolar activity leads to a hierarchical folding that follows the intrinsic bend instability of the active nematic layer. >>

AA << results demonstrate the dynamics of the collapse of orientational order in active nematics and present a new route for controlling active matter by modifying the activity through changing the surrounding environment. >>️

Aleksandra Ardaseva, Ignasi Velez-Ceron, et al. Beyond Dipolar Activity: Quadrupolar Stress Drives Collapse of Nematic Order on Frictional Substrates. arXiv: 2407.03723v3 [cond-mat.soft]. Jan 14, 2025. 

https://arxiv.org/abs/2407.03723

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

Keywords: gst, transition, collapse, active nematics, stress 

# gst: limit cycles and chaos in planar hybrid systems.

<< The main inspiration of (this AA) work is the paper of Llibre and Teixeira (Nonlinear Dyn. 91, No. 1, 249-255, 2018) about Filippov systems formed by two linear centers and having x = 0 as discontinuity line. One of the main conclusions of the paper is that such systems cannot have limit cycles. Actually, either it does not have periodic orbits or every orbit is periodic. Therefore, its dynamics is relatively simple. Inspired by this work and the raising notion of hybrid systems, (AA) wondered what could happen if we allow jumps on the discontinuity line. As a result, (They) discovered not only that limit cycles are allowed with arbitrarily small “perturbations” in the jump, (..), but also that such systems allow chaotic dynamics. Therefore, (AA) conclude that hybrid systems with simple formulation can have rich dynamics. (They) also observe that a complete characterization of the dynamics of X ∈ Xn depends on the characterization of its first return map, which is a piecewise polynomial map on the real line. This, together with the fact that the systems studied here are a generalization of the Filippov systems (..), illustrates that hybrid systems can be seen as a three-fold bridge connecting continuous, piecewise continuous and discrete dynamical systems. >>️

Jaume Llibre, Paulo Santana. Limit cycles and chaos in planar hybrid systems. arXiv: 2407.05151v2 [math.DS]. Oct 1, 2024. 

https://arxiv.org/abs/2407.05151

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

Keywords: gst, limit cycles, chaos, transitions, small perturbations, jumps  

# gst: instability, shocks, and competition interfaces in the Brownian last-passage percolation model

<<  For stochastic Hamilton-Jacobi (SHJ) equations, instability points are the space-time locations where two eternal solutions with the same asymptotic velocity differ. Another crucial structure in such equations is shocks, which are the space-time locations where the velocity field is discontinuous. >>

AA << provide a detailed analysis of the structure and relationships between shocks, instability, and competition interfaces in the Brownian last-passage percolation model, which serves as a prototype of a semi-discrete inviscid stochastic HJ equation in one space dimension. >>

AA << show that the shock trees of the two unstable eternal solutions differ within the instability region and align outside of it. Furthermore, (They) demonstrate that one can reconstruct a skeleton of the instability region from these two shock trees. >>️

Firas Rassoul-Agha, Mikhail Sweeney. Shocks and instability in Brownian last-passage percolation. arXiv:  2407.07866v2 [math.PR]. Oct 18, 2024. 

https://arxiv.org/abs/2407.07866

Also: Brownian last-passage percolation (LPP) model. In: S. GANGULY,  A. HAMMOND. Stability and chaos in dynamical last passage percolation. Jun 7, 2024. 

 https://doi.org/10.1090/cams/35 

Keywords: gst, instability, shock, competition, chaos, percolation

# gst: multiple Pareto-optimal solutions of the dissipation-adaptation trade-off

<< Adaptation refers to the ability to recover and maintain “normal” function on perturbations of internal or external conditions and is essential for sustaining life. Biological adaptation mechanisms are dissipative, i.e., they require a supply of energy such as the coupling to the hydrolysis of ATP. Via evolution the underlying biochemical machinery of living organisms evolved into highly optimized states. However, in the case of adaptation processes two quantities are optimized simultaneously, the adaptation speed or accuracy and the thermodynamic cost. In such cases one typically faces a trade-off, where improving one quantity implies worsening the other. The solution is no longer unique but rather a Pareto set—the set of all physically attainable protocols along which no quantity can be improved without worsening another. >> 

AA << investigate Pareto fronts in adaptation-dissipation trade-offs for a cellular thermostat and a minimal ATP-driven receptor-ligand reaction network. (They) find convex sections of Pareto fronts to be interrupted by concave regions, implying the coexistence of distinct optimization mechanisms. (They) discuss the implications of such “compromise-optimal” solutions and argue that they may endow biological systems with a superior flexibility to evolve, resist, and adapt to different environments. >>️

Jorge Tabanera-Bravo, Aljaz Godec. Multiple Pareto-optimal solutions of the dissipation-adaptation trade-off. 

Phys. Rev. Research 7, 013020. Jan 7, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013020

Also: 'dissipation' in FonT  https://flashontrack.blogspot.com/search?q=dissipation

Also: 'adaptation' in FonT  https://flashontrack.blogspot.com/search?q=adaptation   in Notes (quasi-stochastic poetry) (a) https://inkpi.blogspot.com/search?q=adaptation   

(b) https://inkpi.blogspot.com/search?q=adattamento

Keywords: gst, adaptation, dissipation

# gst: wake interference effects on flapping dynamics of elastic inverted foil.

AA << study the self-induced flapping dynamics of an inverted elastic foil when placed in tandem with a stationary circular cylinder. The effect of wake interference on the inverted foil's coupled dynamics is examined at a fixed Reynolds number (Re) as a function of nondimensional bending rigidity (𝐾B) and the structure-to-fluid mass ratio (𝑚*). >>

AA << results show that there exists a critical 𝐾B (..), above which the downstream foil is synchronized with the unsteady wake, and the cylinder controls the flapping response and the wake vortex dynamics. During synchronization, two additional flapping modes, namely, the small- and moderate-amplitude flapping mode, are observed as a function of decreasing 𝐾B. Below 𝐾B,Cr, the downstream foil undergoes self-induced large-amplitude flapping (LAF) similar to that of an isolated foil counterpart. >>

<< When the dynamics of the downstream foil are analyzed for a range of 𝑚*, (AA) can characterize the response dynamics into two regions: low and high sensitivity. The high-sensitivity region is observed when the dynamics are controlled by the cylinder vortex shedding, i.e., for foils with high stiffness. In this regime, the foil dynamics is negatively correlated with 𝐾B and 𝑚*. >>

<< The low-sensitivity region is observed when the downstream foil is no longer synchronized with the wake and undergoes an LAF response, with dynamics that are weakly correlated with 𝐾B. A nondimensional parameter is proposed that combines the effect of the foil's inertia and elastic forces and can capture the foil's response when it is subjected to wake interference effects. >>

Aarshana R. Parekh, Rajeev K. Jaiman. Wake interference effects on flapping dynamics of elastic inverted foil. Phys. Rev. Fluids 10, 014702. Jan 16, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.014702    arXiv: 2311.09339v3 [physics.flu-dyn]. Apr 25, 2024.   https://arxiv.org/abs/2311.09339

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

Keywords: gst, self-induced flapping dynamics, vortex, elasticity, transitions

# gst: tuning to the edge of instability (in the cochlea)

<< Sound produces surface waves along the cochlea's basilar membrane. To achieve the ear's astonishing frequency resolution and sensitivity to faint sounds, dissipation in the cochlea must be canceled via active processes in hair cells, effectively bringing the cochlea to the edge of instability. But how can the cochlea be globally tuned to the edge of instability with only local feedback? >>

<< Surprisingly, (AA) find the basilar membrane supports two qualitatively distinct sets of modes: a continuum of localized modes and a small number of collective extended modes. Localized modes sharply peak at their resonant position and are largely uncoupled. As a result, they can be amplified almost independently from each other by local hair cells via feedback reminiscent of self-organized criticality. >>

<< However, this amplification can destabilize the collective extended modes; avoiding such instabilities places limits on possible molecular mechanisms for active feedback in hair cells. >>

AA << work illuminates how and under what conditions individual hair cells can collectively create a critical cochlea. >>️

Asheesh S. Momi, Michael C. Abbott, et al. Hair Cells in the Cochlea Must Tune Resonant Modes to the Edge of Instability without Destabilizing Collective Modes. PRX Life 3, 013001. Jan 2, 2025.

https://journals.aps.org/prxlife/abstract/10.1103/PRXLife.3.013001 

Also: sound, music, pause, silence, instability, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, acoustics, bifurcations, sensory processes, sound detection, auditory system, ear, criticality, self-organized criticality, sound, music, pause, silence, instability