# gst: shear v. stretching as drivers for mixing in 3-D porous media flows.

<< ️Solute mixing in porous media results from the interplay between molecular diffusion and the deformation of fluid parcels, which elongates solute elements and steepens concentration gradients in the pore space. >> 

<< ️In three-dimensional porous media, fluid deformation is asymptotically governed by exponential stretching, arising from the chaotic stretching and folding of fluid elements. However, early-time deformation may be dominated by shear, induced by no-slip boundary conditions at grain surfaces, leading to linear elongation. Yet, the persistence and relative contributions of linear shear and exponential stretching to fluid deformation and solute mixing remain poorly understood. >>

<< ️Here, (AA) address this question using numerical simulations of fluid deformation and mixing in body-centered cubic bead packs, where the rate of chaotic stretching can be varied with the direction of flow, while maintaining the same average shear rate. (They) quantify the mean deformation dynamics of elementary surfaces as a function of their initial orientation with respect to streamlines, and their consequences on mixing through Lagrangian methods. >>

<< ️(AA) show that surface elements with certain initial orientations relative to the streamline direction experience a transient phase of shear-dominated deformation at early times, leading to persistently larger deformation compared to those with initial orientations that yield purely exponential growth. By expressing the deformation components in streamline coordinates, (They) derive approximate analytical expressions linking the different components of fluid deformation to shear, helicity, and chaotic stretching. (They) discuss consequences for the mixing of solute sheets and blobs, highlighting generic behaviors as well as differences between these two representations. >>

Manuel Maeritz, Tanguy Le Borgne, Daniel R. Lester, et al. Shear versus stretching as drivers for mixing in three-dimensional porous media flows. Phys. Rev. Fluids 11, 094501. Sep 17, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/4wyw-nkrb

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

Keywords: gst, chaotic advection, fluid deformation, flows in porous media, laminar flows, mixing enhancement, shear flows, chaotic stretching, porous media.

# gst: collective hysteresis and multistability in threshold networks.

<< ️In a mechanistic model of the dawn chorus, Kaye showed that heterogeneous activation thresholds and a shared feedback signal determined by the population's active fraction can produce abrupt collective activation and hysteresis. >>

<< ️(AA) extend this mechanism to a network of interacting agents. Each node has a continuous activation level, and a nonnegative row-stochastic matrix determines how node activities contribute to individual feedback. (They) prove that sufficiently weak feedback yields a unique globally attracting equilibrium. For all feedback strengths, the homogeneous dynamics exactly reproduce Kaye's scalar equation; consequently, network topology does not alter the folds or cusp of the homogeneous branch, and no heterogeneous mode becomes unstable before the homogeneous mode. >>

<< ️For equitable partitions, the network admits an exact quotient system in which nodes within a block receive the same aggregate input from every block. When blocks are uncoupled, the quotient reduces to independent copies of Kaye's scalar equation. (AA) show that every assignment of stable scalar equilibria to blocks persists under sufficiently weak interblock coupling, producing a combinatorial family of stable quotient equilibria that lift to stable full-network equilibria and remain under small perturbations that break exact equitability. >>

<< ️For two symmetrically coupled blocks, branches with unequal block activities terminate at a pair of symmetry-related cusp bifurcations. Near the onset of bistability, (AA) derive scaling laws for the interblock coupling at which these bifurcations occur, the activity difference between the blocks at bifurcation, and the corresponding shift of the external stimulus from the scalar cusp. Numerical continuation confirms the scaling laws for gamma, logistic, and normal threshold distributions. >>

Moses Boudourides. Collective Hysteresis and Multistability in Threshold Networks. arXiv: 2609.10580v1 [cs.SI]. Sep 5, 2026.

https://arxiv.org/abs/2609.10580

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

Keywords: gst, hysteresis, collective hysteresis, networks, threshold networks, stability, bistability, multistability, randomness, small perturbations, bifurcations, cusp bifurcations, Kaye's dawn chorus, stochasticity, heterogeneous activation thresholds, weak feedbacks, shared feedback signals, attracting equilibrium.

# gst: reconstructing the information processing capacity of physical systems from noisy observations.

<< ️Driven dynamical systems can compute when their transient states encode complex transformations of past inputs. The information processing capacity (IPC) framework allows for a detailed accounting of these computational properties, however its interpretation in noisy systems has remained incomplete. >>

<< ️In this work, (AA) clarify how noise affects the IPC and how one can reconstruct the noiseless IPC. First, (They) show how to distinguish the dynamics of an unperturbed system from the noise-free component of the stochastic dynamics: The IPC measured for responses averaged over noise realizations is in general not the same as the IPC of the unperturbed system. (They) explicitly demonstrate that noise can redistribute computational capacity and sometimes even enhance performance on particular tasks, rather than merely degrading a fixed computation. (They) then introduce covariance reconstruction by orthogonal projection (CROP), which reconstructs the covariance and IPC of the noise-free component directly from noisy observations, without requiring a detailed model of either the system or the noise. >>

<< ️At fixed total measurement budget, numerical tests on a classical nonlinear reservoir show that CROP estimates the noise-free IPC more accurately than the standard practice of ensemble averaging over repeated trials. (AA) find the same advantage in a quantum reservoir subject to unavoidable measurement noise. (Their) results provide a general route to recovering the computational structure of noisy physical systems from finite observations. >>

Shun Kotoku, Rodrigo Martínez-Peña, Takatomo Mihana, et al. Reconstructing the information processing capacity of physical systems from noisy observations. arXiv: 2609.11268v1 [nlin.AO]. Sep 10, 2026.

https://arxiv.org/abs/2609.11268

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

Keywords: gst, noise, information processing capacity (IPC), covariance reconstruction by orthogonal projection (CROP), stochasticity.

# gst: thermodynamics of bouncing grains.

<< When a horizontal plate vibrates strongly enough, it causes small particles such as sand grains to continually bounce on it and, over time, to diffuse across its surface. This phenomenon is the cause of the well-known Chladni figure, which is drawn by a higher density of grains gathering along the nodal lines of a resonating elastic plate. >>

<< Using a heterogeneous, nonresonating plate, (AA) investigate experimentally this type of diffusion. (They) find that, for the most part, it is comparable to classical molecular diffusion. (They) can define a temperature for the bouncing grains, and the system then obeys the fluctuation-dissipation theorem. (They) also recover Maxwell-Boltzmann statistics at equilibrium, when temperature is uniform. >>

<< However, when temperature varies across the vibrating plate, the microscopic details of the grains' dynamics affect their macroscopic behavior: Fick's law, for instance, no longer applies. Instead, (Their) experiments support a new transport relation that was recently proposed to represent diffusion in Chladni's experiment. >>

<< Finally, (AA) propose an expression for the heat flux associated to the nonequilibrium steady state predicted by this new relation and test it against observations. >>

O. Devauchelle, P. Popović, P. Szymczak, et al. Thermodynamics of bouncing grains. Phys. Rev. E 114, 025420. Aug 24, 2026.

https://journals.aps.org/pre/abstract/10.1103/zlsc-w7m4

arXiv: 2606.05930v1 [cond-mat.stat-mech]. Jun 4, 2026.

https://arxiv.org/abs/2606.05930

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

Keywords: gst, particles, active brownian particles, brownian ratchet, granular materials, bouncing grains, vibrating plate, molecular diffusion, fluctuation-dissipation.

# gst: hierarchy in Gilbert's tessellation; multifractal behavior.

<< ️(AA) have introduced two types of hierarchies in a classical Gilbert tessellation. The cascading process that follows gives rise, in both cases, to a tile area distribution function that fits surprisingly well with a generalized gamma function. The latter is a truncated power function which, in turn, in the spirit of Brown’s sequential fragmentation theory, is derived from a stretched exponential hazard function that is also truncated. >>

<< ️This theoretical finding finds a natural counterpart in the experimental observations of Kooij and coworkers [S. Kooij et al., Nat. Commun. 12, 2521 (2021)], according to which the fragmentation of a brittle sample follows two distinct regimes: a random breakup that gives rise to a simple exponential distribution of mass fragments (canonical Gilbert), whereas a hierarchical crushing leads to a power-law distribution (hierarchical Gilbert, in fact g3(x) ∼ x^(c−1) for x → 0). >>

<< ️(AA) study demonstrates that the DG and HG cascade processes (i.e. Dichotomous Gilbert (DG), Hierarchical Gilbert (HG)) display a multifractal nature. Both models produce a heterogeneous distribution with different characteristics, quantitatively described by two different multifractal spectra. A direct, quantitative comparison between (Their) geometric models and specific experimental datasets remains, at present, an open challenge and would require fragmentation experiments capable of resolving a sufficiently wide range of fragment sizes to reliably probe the hierarchy-induced effect. >>

E.Consolini, B.Bonanni, M.Fanfoni. Hierarchy in Gilbert's tessellation: Multifractal behavior. Phys. Rev. E 114, 034120. Sep 11, 2026.

https://journals.aps.org/pre/abstract/10.1103/p5xq-nj2g

Also: fracture, crack, random, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, fracture, crack, randomness, fragmentation process, fragment-size distribution, scale-free behavior, 2-D random tessellation, fractals, multifractal systems, multifractal scaling. 

# behav: collective turns in spinless flocks.

<< ️Using a minimal aggregation-based model, (AA) address the efficient information transfer observed in natural flocks during collective turns. In (Their) system, the turning signal emitted by a single individual propagates throughout the collective primarily at a constant speed. >>

<< ️To characterize the source of this capability, (AA) analyze the system in the continuum limit. Thus, (They) demonstrate that wave-propagating features arise solely from the nonreciprocal nature of interactions. (They) explore spectral anomalies that emerge due to this mechanism and provide an explanation through a perturbative analysis. >>

<< ️Remarkably, within this scenario, the description of velocity fluctuations is found to follow a structure analogous to a Born approximation. (Their) model can be extended to study other physical contexts exhibiting polar order, and (Their) arguments can be tested in natural systems. >>

Joao Lizárraga, Marcus A. M. de Aguiar. Collective turns in spinless flocks. Phys. Rev. E 114, 035401. Sep 1, 2026.

https://journals.aps.org/pre/abstract/10.1103/6976-lcw7

arXiv: 2511.17804v2 [nlin.AO]. Nov 21, 2025.

https://arxiv.org/abs/2511.17804

Also: behav, flock, flocking, fluctuations, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: behavior, flock, flocking, fluctuations, waves, collective turns, turning signals.

# life: early warning signals can vanish or amplify; dimensionality in complex systems.

<< Early warning signals (EWS), such as increasing variance and autocorrelation, are widely used to anticipate critical transitions associated with saddle-node bifurcations. However, real-world systems are often high-dimensional and multiscale, potentially altering the classical behavior of EWS. >>

<< Here, (AA) investigate how dimensionality, inertia, and red noise influence the detectability of EWS prior to tipping points. (They) show that when observations are not aligned with the critical direction, stable dynamics in orthogonal directions can mask EWS until very near the bifurcation. >>

<< (AA) further demonstrate that second-order dynamics with damping modify the autocorrelation structure and may either enhance or reduce signatures of critical slowing down. >> 

<< Finally, (AA) study how colored noise influences EWS. (Their) results show that the presence and strength of EWS are not universal properties of tipping systems but depend critically on system geometry and stochastic forcing, implying that the absence of detectable EWS does not necessarily rule out an approaching critical transition. >>

Susanne Ditlevsen, Peter Ditlevsen. Early Warning Signals Can Vanish or Amplify: Dimensionality in Complex Systems. arXiv: 2609.01164v1 [math.DS]. Sep 1, 2026.

https://arxiv.org/abs/2609.01164

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

Keywords: gst, noise, transitions, early warning signals (EWS), criticality, saddle-node bifurcations, dimensionality, inertia, red noise, colored noise, tipping points, critical slowing down, stochastic forcing.