# gst: stabilities in the attachment of a particle to a pendant droplet.

<< ️Attachment of a particle to a pendant drop was experimentally investigated by Feng et al. (2022)]. The attachment force on the particle, consisting of the surface tension force and the pressure force, can overcome the gravity force. The attachment in equilibrium is possibly hard to maintain in practice due to instabilities. >>

<< This (AA) paper aims to discover the condition for the particle to be successfully attached under the liquid drop (bridge) through analyzing the stabilities of the capillary system. With disturbances potentially existing for both the liquid bridge and the particle, the two corresponding types of stabilities are studied. >>

<< Considering the cases with liquid surfaces checked to be stable, (AA) find four regimes for the attachment of the particle: the regimes of stable attachment, possibly stable attachment, overloaded attachment, and nonphysical attachment. Only the first two regimes mean feasible attachments in practice. (Their) prediction of feasible attachments agrees well with Feng et al., indicating the validity of (Their) stability theory. Whether for fixed-density particles of different sizes or fixed-size particles of different densities, the attachment capability for the liquid bridge first decreases, then increases, and decreases again as the volume of the liquid bridge increases. This can guide practice for lifting particles of higher weight with the pendant drop. >>

Wanqiu Zhang, Fei Zhang, Xinping Zhou. Stabilities in the attachment of a particle to a pendant droplet. Phys. Rev. Fluids 11, 084001. Aug 7, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/b63k-qk8s

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

Keywords: gst, drops, droplets, droploids, particles, stability, fluid-particle interactions, interfacial flows, liquid bridges, surface & interfacial phenomena.

# gst: escape over a saddle by colored noise.

<< ️Stochastic dynamical systems allow modeling of transitions induced by random disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. While the small-noise limit is well-described by the large deviation principle, existing computational methods often struggle with stochastic forcings any more complicated than nondegenerate Gaussian white noise, and with unbounded time intervals. >>

<< ️The primary innovations of this (AA) work are extending the framework to cater for colored and degenerate forcing and unbounded time horizons—scenarios that are physically realistic but numerically challenging. (They) cater for degenerate noise by using the Hamiltonian optimal control method. (They) cater for a class of colored noises by using linear filters on white noise. (They) cater for infinite time horizon by introducing the method of division (MOD), a computational approach for approximating rare transition events, including their most likely paths and the exponential scaling laws of their transition rates. >>

<< ️The effectiveness of MOD and the above approaches to colored noise, is demonstrated by illustration on two examples: an inverted double-well potential and a simplified roll-heave model for ship capsize. >>

Jiayao Shao (邵家瑶), Tobias Grafke, Robert S. MacKay. Escape over a saddle by colored noise: Theory and numerics. Phys. Rev. E 114, 024210. Aug 12, 2026.

https://journals.aps.org/pre/abstract/10.1103/w8dd-9cqg

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

Keywords: gst, escape, noise, randomness, stochasticity, transitions, noise-induced transitions, method of division (MOD), inverted double-well potential, simplified roll-heave model, large deviation & rare event statistics.

gst: nonreciprocal dynamics with weak noise: aperiodic “Escher cycles” and their quasipotential landscape.

<< ️(AA) present an explicit construction of the Freidlin-Wentzell quasipotential of a stochastic system with two degrees of freedom and nonreciprocal interactions. This model undergoes noise-induced transitions between four metastable attractors, forming recurrent but aperiodic “Escher cycles,” similar to the cyclic nucleation dynamics observed in the nonreciprocal Ising model. >>

<< (AA) calculate the quasipotential analytically to first order in nonreciprocality. (They) characterize it along a one-dimensional reaction coordinate that connects the attractors, and (They) also obtain the full two-dimensional landscape, at leading order in perturbation theory. >>

<< ️The resulting landscapes feature flat regions and extended plateaus, together with nondifferentiable switching lines. These singular structures arise from two geometric mechanisms: the handover of dominance between competing transition paths, and the competition between basins of attraction. The system provides a rare case where the geometry of nonequilibrium rare events can be fully resolved, and a simple analytically tractable example of a quasipotential in more than one coordinate that captures a rich set of nonequilibrium features. >>

Janik Schüttler, Robert L. Jack, Michael E. Cates. Nonreciprocal dynamics with weak noise: Aperiodic “Escher cycles” and their quasipotential landscape. Phys. Rev. E 114, 024104. Aug 3, 2026.

https://journals.aps.org/pre/abstract/10.1103/slp9-rd27

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

Keywords: gst, noise, randomness, stochasticity, transitions, singularity, nonreciprocal interactions, noise-induced transitions, metastable attractors, Escher cycles, perturbation theory, escape problems, large deviation & rare event statistics. 

# gst: apropos of persistence or extinction, lag-induced critical transitions to extinction in replicating systems; the 𝜏-tipping mechanism.

<< Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are classically governed by mutation rates and fitness landscape topographies, giving rise to error thresholds and lethal mutagenesis. >>

<< Motivated by experimental evidence that polymerase-targeting antivirals limit replication, (AA) analyze replicating systems with explicit time lags in replication-enzyme availability by means of delay differential equations. (Their) approach is not equivalent to a simple renormalization of the rate of replication, since explicit delays introduce memory and temporal nonlocality into the dynamics. (They)  identify a lag-induced critical transition driven by the loss of temporal coordination between genome expression and replication. >>

<< At fixed mutation and replication rates ensuring persistence, populations cross an extinction threshold solely due to replication delays. In (Their) delay-extended quasispecies model, the timing of replicase availability emerges as an independent dynamical control parameter, defining a route to extinction that is fundamentally distinct from transitions driven by mutation rates or replicative fitness. >>

<< These (AA) results further suggest that perturbing the temporal coordination of viral replication may provide an alternative antiviral strategy for driving viral populations toward collapse. More generally, (They) propose that the extinction mechanism described here constitutes a form of lag-time-induced tipping, which (They) denote as 𝜏-tipping. >>

Edward A. Turner, Francisco Crespo, Joan Gimeno, et al. Lag-induced critical transitions to extinction in replicating systems: the 𝜏-tipping mechanism. Phys. Rev. E 114, 024401. Aug 5, 2026.

https://journals.aps.org/pre/abstract/10.1103/gyd9-ctnc

arXiv: 2603.02036v1 [q-bio.PE]. Mar 2, 2026. 

https://arxiv.org/abs/2603.02036

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

Keywords: gst, transitions, pause, silence, virus, error, collapse, genomes, RNA virus, replication, replicating systems, enzymatic amplification, criticality, persistence, extinction, mutation rates, fitness landscape topographies, error threshold, time-delay systems, lag-time-induced tipping, lag-induced critical transition, loss of temporal coordination.

# behav: noise-induced stability of insect swarms.

<< ️Flying insect swarms exhibit cohesion without the local velocity alignment observed in flocks of birds or schools of fish. The interaction rules and channels of communication between insects that lead to collective behavior have not yet been determined. >>

<< ️(AA) propose a theoretical model based on acoustic communication between swarm members, where each individual is attracted to a weighted mean field of its neighbors. (They) demonstrate that this simple framework can describe a wide range of swarming dynamics, including a phenomenon where pairs of insects break free from the swarm in a helical orbit around each other. >>

<< ️Counterintuitively, (Their) numerical model suggests that stochastic noise enhances the stability of an insect swarm, as it interferes with pair formation. >>

<< Finally, (AA) demonstrate that a specific species of malarial mosquito produces swarms that reside on the edge of a transition to instability. (Their) study shows that fairly simple local interaction rules can be sufficient to describe the collective behavior of swarming biological systems. >>

Justin Faber, Annabelle Boots, Dolores Bozovic. Noise-induced stability of insect swarms. arXiv: 2608.00314v2 [physics.bio-ph]. Aug 7, 2026.

https://arxiv.org/abs/2608.00314

Also: swarm, behavior, noise, instability, transition, sound, jazz, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: behavior, swarm, noise, instability, transitions, sound, jazz, dance, flying insects, collective behavior, acoustic communication, weighted mean field of neighbors.

# gst: survival probability of particles inside the lemon billiard.

<< ️(AA) study the escape of particles in the lemon billiard, a two-parameter family of billiard systems defined by the intersection of two identical circles. Using numerical simulations, (They) explore how the survival probability depends on the position and size of the hole, as well as on the billiard shape parameter. >>

<< ️(AA) find that the survival probability exhibits a two-stage decay pattern: an initial exponential regime followed by a long-time power-law tail, a signature of the stickiness effect. (Their) results show that the short-time exponential decay rate follows a power-law dependence on the hole size, with different scaling exponents for holes placed in chaotic regions versus mixed phase-space regions. For holes located in mixed phase-space regions, the decay exponent of the long-time power-law tail remains approximately constant, while the amplitude follows a power-law scaling with hole size. >>

<< ️(They) also examine the dependence of short-time exponential decay rate on the billiard shape parameter and observe scaling behavior for small values of this parameter, which breaks down as the parameter increases. >>

Daniel Borin, Edson Denis Leonel, Diego Fregolent Mendes de Oliveira. Survival probability of particles inside the lemon billiard. Phys. Rev. E 114, 014224. Jul 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/md5j-ggyd

arXiv: 2601.13000v1 [nlin.CD]. Jan 19, 2026.

https://arxiv.org/abs/2601.13000

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

Keywords: gst, billiard, particles, chaos, transitions, survival probability, two-stage decay pattern, stickiness effect, scaling behavior, scaling laws of complex systems. 

# gst: apropos of bluff-body wakes, effect of centerline separation on a vortex dominated wake.

<< A previously undocumented Reynolds-number-dependent transition is identified in the wake of a rounded-edge slanted afterbody, from a centerline-separated to a novel centerline-attached vortex state. The transition produces a pronounced drag reduction through the collapse of the centerline recirculation region as the upstream boundary layer becomes turbulent. These (AA) findings explore experimental evidence linking laminar separation bubble dynamics, shear-layer instability, and wake-state transitions in this canonical bluff-body geometry. >> ( APS Editor, https://journals.aps.org/prfluids/recent/ )

Rhylan A. Huss, Farrukh S. Alvi. Effect of centerline separation on a vortex dominated wake. Phys. Rev. Fluids 11, 074702. Jul 28, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/bn64-wtlz

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

Keywords: gst, vortex, transition, 

bubble, laminar separation bubble dynamics, shear-layer instability, wake-state transitions.