# gst: apropos of modulational instabilities, the case of vortex-ring quantum droplets in a radially-periodic potential.

FIG. 11: (Color online) Typical examples of stable nested patterns with soliton and vortex QDs (quantum droplets)  which were created in adjacent radial troughs. In panels (a1-b4) the pattern was created from the initial dynamical states with parameters (N,S,On) = (46,0,2) and (N,S,On) = (35,1,1) in the outer and inner troughs, respectively. In panels (c1-d4) the input was taken with parameter sets (N,S,On) = (120,1,3) and (N,S,On) = (46,0,2) in the outer and inner troughs.

AA << establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates. >>️

<< another noteworthy option is to construct a two-ring complex in which one vortex-ring component is subject to the MI  (modulational instability), hence it is replaced by an azimuthal soliton (or maybe several solitons), (..), while the vortex component trapped in another potential trough avoids the azimuthal MI and remains essentially axisymmetric. >>️

<< Examples of such heterogeneous robust states, produced by simulations of Eq. (3), are displayed in Fig. 11. Panels 11(a1-b4) show a complex in which the MI takes place in the outer circular trough, producing an azimuthal soliton which performs rotary motion, while the inner vortex ring is  modulationally stable. An opposite example is produced in Figs. 11(c1-d4), where the outer vortex ring remains stable against azimuthal perturbations, while the MI creates a soliton exhibiting the rotary motion in the embedded (inner) circular trough. The rotation direction of the soliton is driven by the vorticity sign of the underlying QD (quantum droplet). It is relevant to mention that the multi-ring potential considered here holds different vortex-ring or azimuthal-soliton states nearly isolating them from each other. (..) An additional problem, which is left for subsequent analysis, is interplay between adjacent radial modes in the case when the separation between the adjacent rings is essentially smaller. >>️

Bin Liu, Yi xi Chen, et al. Vortex-ring quantum droplets in a radially-periodic potential. arXiv: 2212.05838v1 [nlin.PS]. Dec 12, 2022.

https://arxiv.org/abs/2212.05838

Also

keyword 'drop' | 'droplet' | 'droploids' in FonT

https://flashontrack.blogspot.com/search?q=drop

https://flashontrack.blogspot.com/search?q=droplet

https://flashontrack.blogspot.com/search?q=droploids

keyword 'goccia' in Notes 

(quasi-stochastic poetry): 

https://inkpi.blogspot.com/search?q=goccia

keyword 'instability' | 'instabilities' in FonT

https://flashontrack.blogspot.com/search?q=instability

https://flashontrack.blogspot.com/search?q=instabilities

keyword 'instabile' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=instabile

Keywords: gst, drop, droplet, vortex, vortices, vortexes, vorticity, instability,  modulational instabilities

# gst: intermittent large-intensity pulses (LIE) due to instabilities in quasiperiodic motion (in Zeeman laser)

AA << report intermittent large-intensity pulses that originate in Zeeman laser due to instabilities in quasiperiodic motion, >>

<< one route follows torus-doubling to chaos and another goes via quasiperiodic intermittency in response to variation in system parameters. >>

<< During quasiperiodic intermittency, the temporal evolution of the laser shows intermittent chaotic bursting episodes intermediate to the quasiperiodic motion instead of periodic motion >>

<< The intermittent bursting appears as occasional large-intensity events (LIE). In particular, this quasiperiodic intermittency has not been given much attention so far from the dynamical system perspective, in general. >>

S. Leo Kingston, Arindam Mishra, Marek Balcerzak, Tomasz Kapitaniak, Syamal K. Dana. Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser. arXiv: 2109.11847v1 [nlin.CD]. Sep 24, 2021. 

https://arxiv.org/abs/2109.11847

keywords: gst, quasiperiodic motion, intermittency, quasiperiodic intermittency, instability, chaos.

# gst: apropos of transitions, three distinct new families of long-wave instabilities and potential new pathways to turbulence.

AA << reveal three previously unknown instabilities, distinct from the well-known Kelvin-Helmholtz Instability (KHI) and Holmboe Wave Instability (HWI), in that they have longer wavelengths (..) and often slower growth rates. >>

<< The circumstances under which turbulence can persist in strongly stratified flows remains a fascinating debate within the community. [AA] demonstrated that weakly unstable (very) long waves may trigger turbulence and mixing after long periods of time, even under initially very strongly stratified conditions. >>

Lu Zhu, Amir Atoufi, Adrien Lefauve, Rich R. Kerswell, P. F. Linden. Long-wave instabilities of sloping stratified exchange flows. arXiv:2309.10056v1 [physics.flu-dyn]. Sep 18, 2023.

https://doi.org/10.48550/arXiv.2309.10056

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

Keywords: gst, waves, instability, long-wave instability, transition, turbulence, chaos

# gst: approaching the complex mechanics of crumpled sheets

<< Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as logarithmic relaxation, emission of crackling noise, and memory retention. >>️

<< the response of crumpled sheets to cyclic strain is intermittent, hysteretic, and encodes a memory of the largest applied compression. (..) these behaviours emerge due to an interplay between localized and interacting geometric instabilities in the sheet. >>

<< after training multiple memories can be encoded, a phenomenon known as return point memory. >>

AA << study lays the foundation for understanding the complex mechanics of crumpled sheets, and presents an experimental and theoretical framework for the study of memory formation in systems of interacting instabilities. >>️️

Dor Shohat, Daniel Hexner, Yoav Lahini. Memory from coupled instabilities in crumpled sheets. arXiv: 2109.05212v1 [cond-mat.soft]. Sep 11, 2021.

https://arxiv.org/abs/2109.05212

keywords: gst, sheet, crumpled sheets, instability, bistability, memory, return point memory

# gst: apropos of instabilities, viscoelastic liquid bridges can be destabilized by torsion.

<< Liquid bridges are formed when liquids are constrained between two (or more) surfaces via the capillary force. They appear in a wide range of contexts including biology, medicine, and engineering. In the context of biology, liquid bridges enable animals like geckos to adhere to vertical walls (..) >>

<< By experiment and simulation, (AA) report that viscoelastic liquid bridges made of constant viscosity elastic liquids, a.k.a. Boger fluids, can be effectively destabilized by torsion. Under torsion, the deformation of the liquid bridge depends on the competition between elastocapillarity and torsion-induced normal stress effects. When the elastocapillary effect dominates, the liquid bridge undergoes elastocapillary instability and thins into a cylindrical thread, whose length increases and whose radius decays exponentially over time. When the torsion-induced normal stress effect dominates, the liquid bridge deforms in a way similar to edge fracture, a flow instability characterized by the sudden indentation of the fluid's free surface when a viscoelastic fluid is sheared at above a critical deformation rate. The vertical component of the normal stress causes the upper and lower portions of the liquid bridge to approach each other, and the radial component of the normal stress results in the liquid bridge thinning more quickly than under elastocapillarity. Whether such quick thinning continues until the bridge breaks depends on both the liquid bridge configuration and the level of torsion applied. >>️

San To Chan, Stylianos Varchanis, et al. Torsional instability of constant viscosity elastic liquid bridges. Soft Matter, 2022,18, 1965-1977. doi: 10.1039/ D1SM01804C. Feb 7, 2022. 

https://pubs.rsc.org/en/content/articlelanding/2022/SM/D1SM01804C

image: https://twitter.com/softmatter/status/1504473129074126851

Also

keyword 'instability' | 'instabilities' in FonT

https://flashontrack.blogspot.com/search?q=instability

https://flashontrack.blogspot.com/search?q=instabilities

keyword 'instabile' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=instabile

keyword 'torsione' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=torsione

keywords: instability, torsion, torsional instability, viscoelastic liquid, bridge

# gst: apropos of transitions, perspectives on viscoelastic flow instabilities; the 'porous individualism'

<< given the observation that disorder can suppress the transition to elastic turbulence in 2D porous media (..), it has been unclear whether and how this transition manifests in disordered 3D media — though elastic turbulence has been speculated to underlie the long-standing observation that the macroscopic flow resistance of an injected polymer solution can abruptly increase above a threshold flow rate in a porous medium, but not in bulk solution >>️

AA << found that the transition to unstable flow in each pore is continuous, arising due to the increased persistence of discrete bursts of instability above a critical value of the characteristic (Weissenberg no.) Wi; however, the onset value varies from pore to pore. This observation that single pores exposed to the same macroscopic flow rate become unstable in different ways provides a fascinating pore-scale analog of “molecular individualism” [P.  De Gennes, Molecular individualism. Science 276, 1999–2000 (1997)], in which single polymers exposed to the same extensional flow elongate in different ways; the authors therefore termed it “porous individualism”, although it is important to note that here, this effect is still at the continuum (not molecular) scale. Thus, unstable flow is spatially heterogeneous across the different pores of the medium, with unstable and laminar regions coexisting >>

AA << quantitatively established that the energy dissipated by unstable pore-scale fluctuations generates an anomalous increase in flow resistance through the entire medium that agrees well with macroscopic pressure drop measurements. >>

Sujit S. Datta, Arezoo M. Ardekani, et al. Perspectives on viscoelastic flow instabilities and elastic turbulence. arXiv: 2108.09841v1 [physics.flu-dyn]. Aug 22, 2021. 

https://arxiv.org/abs/2108.09841

Also

keyword 'transition' | 'transitional' in FonT

https://flashontrack.blogspot.com/search?q=transition

https://flashontrack.blogspot.com/search?q=transitional

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=transition

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transizioni

keywords: gst, droplet, fluctuations, disorder, instability, viscoelastic flow instability, turbulence, elastic turbulence, individualism, porous individualism, transition

# gst: when turbulence is driven by a strongly compressive guide

<< it is not fully understood how shocks drive turbulence, in particular whether shock driving is a more solenoidal (rotational, divergence-free) or a more compressive (potential, curl-free) mode of driving turbulence. >>️

<< Here, (AA) use hydrodynamical simulations of a shock inducing turbulent motions in a structured, multi-phase medium. >>️

<< Using simulations in which a shock is driven into a multi-phase medium with structures of different sizes and Γ<1, (AA) find b∼1 for all cases, showing that shock-driven turbulence is consistent with strongly compressive driving. >>️

Saee Dhawalikar, Christoph Federrath,  et al. The driving mode of shock-driven turbulence. arXiv:2205.14417v1 [astro-ph.GA]. May 28, 2022. 

https://arxiv.org/abs/2205.14417

Also

keywords 'turbulence' in FonT

https://flashontrack.blogspot.com/search?q=turbulence

keywords 'turbolento' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=turbolento

keyword 'waves' in FonT

https://flashontrack.blogspot.com/search?q=waves

keyword 'onda' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=onda

keyword 'instability' | 'instabilities' in FonT

https://flashontrack.blogspot.com/search?q=instability

https://flashontrack.blogspot.com/search?q=instabilities

keyword 'instabile' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=instabile

Keywords: gst, turbulence, instability, waves, shock waves

# gst: apropos of vibrating pivots, driving a damped coplanar double pendulum.

AA << present results of linear and nonlinear motions of a parametrically driven coplanar double pendulum with velocity-dependent damping. The equations of motion of a damped double pendulum of unequal masses with its pivot vibrated vertically are different from those obtained under gravity modulation. 

Linear stability analysis shows that tongue-shaped marginal stability curves divide the plane of driving parameters into multiple regions of subharmonic and harmonic instabilities. The instability zones for one normal mode overlap with those for the other. 

The double pendulum may oscillate or rotate about its pivot harmonically or subharmonically. The limit cycles corresponding to the normal mode oscillations of a double pendulum of equal masses are squeezed into a line in its configuration space. 

For unequal masses, two marginal curves for subharmonic instabilities merge to form a double-well shaped curve in the presence of damping, which is qualitatively new. The pendulum shows driving amplitude sensitive multi-period complex oscillations for driving parameters near the extrema of the merged instability zones and boundaries of the overlapping zones. 

For larger driving amplitude, the pendulum shows subharmonic, harmonic or chaotic rotations. >>

️

Rebeka Sarkar, Krishna Kumar, Sugata Pratik Khastgir. Parametrically driven damped coplanar double pendulum. arXiv:2208.03292v1 [physics.class-ph]. Aug 2, 2022. 

https://arxiv.org/abs/2208.03292

Also

keyword 'pendulum' in FonT

https://flashontrack.blogspot.com/search?q=pendulum

keyword 'pendolo' | 'pendola' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=pendolo

https://inkpi.blogspot.com/search?q=pendola

Keywords: gst, pendulum, double pendulum, instability, chaos, chaotic rotations

# gst: transitions by coupled instabilities

AA << present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. (They)  show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. >>

Valeri Frumkin, Shreyas Gokhale. Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves. Phys. Rev. E 108, L012601. July 17, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.L012601

Also: parrondo, tit-for-tat, game, transition, chaos, in https://www.inkgmr.net/kwrds.html

Keywords: parrondo, tit-for-tat, game,  transition, chaos

# gst: kirigami exposed to external flows.

<< Kirigami patterned materials have found several applications in recent years due to their ability to assume complicated shapes and exhibit emergent physical properties when exposed to external forces. >>️

<< Consisting of an array of cuts in a thin material, fabrication of these patterns can be quite simple. Here (AA) show that when they are placed in fluid flow, kirigami cut sheets with various patterns produce a verity of flow patterns in the wake. Through several sets of experiments, (AA) show that the kirigami sheets placed in flow can undergo static or dynamic flow-induced instabilities as a result of which they can buckle or undergo limit cycle oscillations, or they can remain stable while undergoing very large elongations. >>️

<< The ability to create controlled small-scale vortex shedding, induce desired flow-induced instabilities on structures, and form specifically-angled jets will enable several future applications in flow mixing (e.g., by producing small vortices in uniform flow at low Reynolds numbers), flow control (e.g., by controlling the direction and the number of jets that are produced downstream), and underwater soft robotics (e.g., by imposing desired flow-induced oscillations on structures). >>

️

Adrian G. Carleton, Yahya Modarres-Sadeghi. Kirigami Sheets in Fluid Flow.  arXiv: 2311.09381v1 [physics.flu-dyn]. Nov 15, 2023. 

https://arxiv.org/abs/2311.09381

Also: kirigami, origami, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, kirigami, origami, fluid flows, vortex

# gst: elastic instabilities, a morphing model to quickly trap anything (in 100msec), the Venus flytrap (Dionaea muscipula)

<< The Venus flytrap (Dionaea muscipula) takes only 100 milliseconds to trap its prey. Once their leaves, which have been transformed into snap traps, have closed, insects can no longer escape. >>

<< the trap of the carnivorous plant is under mechanical prestress. In addition, its three tissue layers of each lobe have to deform according to a special pattern. >>

<< In order to close correctly, the traps also had to consist of three layers of tissue: an inner which constricts, an outer which expands, and a neutral middle layer. >>

Albert Ludwigs. Biomechanical analyses and computer simulations reveal the Venus flytrap snapping mechanisms. University of Freiburg. Jun 23, 2020.

https://phys.org/news/2020-06-biomechanical-analyses-simulations-reveal-venus.html

Renate Sachse, Anna Westermeier, et al. Snapping mechanics of the Venus flytrap (Dionaea muscipula). PNAS. doi: 10.1073/ pnas.2002707117. Jun 22, 2020. 

https://www.pnas.org/content/early/2020/06/19/2002707117

Also

Dionaea muscipula, with precision. FonT. Feb 2, 2016. 

https://flashontrack.blogspot.com/2016/02/rmx-s-phyto-dionaea-muscipula-with.html

# gst: self-buckling and self-writhing of semi-flexible Entities (among P. mirabilis)

<< Multi-flagellated microorganisms can buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configurations and steady-state dynamics then emerge which depend on the organism's mechanical properties and on the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod and coupling the mechanics to a dynamically evolving flagellar orientation field, (AA) derive the Euler-Poincaré equations governing dynamics of the system, and rationalize experimental observations of buckling and writhing of elongated swarmer P. mirabilis cells. >>

<< A sequence of bifurcations is identified as the body is made more compliant, due to both buckling and torsional instabilities. The results suggest that swarmer cells invest no more resources in maintaining membrane integrity than is necessary to prevent self-buckling. >>

️

Wilson Lough, Douglas B. Weibel, et al. Self-buckling and self-writhing of semi-flexible microorganisms. arXiv: 2211.04381v1 [cond-mat.soft]. Nov 8, 2022. 

https://arxiv.org/abs/2211.04381

Also 

keyword 'swimming' in FonT

https://flashontrack.blogspot.com/search?q=swimming

Keywords: gst, motility, swarm, swarming, swarmer, swim, swimming, swimmer, buckling, writhing. 

# gst: an atomic imaging of a (slow) crack

AA << successfully imaged the snapping of individual atomic bonds in a one-atom-thick sheet of rhenium disulfide ( ReS2) using scanning transmission electron microscopy. (STEM) >>

<< Because of its unusual chemistry, Re forms a 2D lattice with "lanes" that guide cracks, allowing the cracks to propagate with ease. The heavy element also efficiently deflects electrons, providing the signal needed to gain clear images. The study is a remarkable example of how a specific material can provide insight into the universal behavior of matter. >>

<< Because of its strong scattering, ReS2 provides an ideal target for STEM. (Interestingly, tungsten, the periodic-table neighbor of Re, has just one fewer proton and is routinely used in electron microscopy to stain viruses and bacterial flagella.)  >>

<< By measuring the deformation of the lattice around the crack, the team showed that the tearing stresses were concentrated around the crack tip. The stresses then decayed as the inverse square root of the distance from the tip, a finding that matches predictions for macroscopic materials. Using these measurements, the team defined a stress intensity threshold for cracks to propagate. >>

<< The images taken by Huang and colleagues used seconds-long exposure times, meaning they could only follow the propagation of the slowest crack (those that moved at a few angstroms per second). There is much interest in how faster cracks behave, as these cracks are subject to instabilities, meaning they can deviate from a straight line or form branches, for example. To observe faster cracks, future experiments could use reduced exposure times. >>

Itamar Kolvin. Atomic Imaging of Cracks. Physics 13, 193. Dec 9, 2020. 

https://physics.aps.org/articles/v13/193

Lingli Huang, Fangyuan Zheng, et al. In Situ Scanning Transmission Electron Microscopy Observations of Fracture at the Atomic Scale. Phys. Rev. Lett. 125, 246102. Dec 9, 2020.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.246102

Also

(+)  the intriguing dynamics of a crack. Nov 7, 2017. 

https://flashontrack.blogspot.com/2017/11/gst-intriguing-dynamics-of-crack.html

(+) multiple cracks, simultaneously ... Oct 23, 2016.

https://flashontrack.blogspot.com/2016/10/s-gst-multiple-cracks-simultaneously.html

(+) onda criptica. May 22, 2005 (quasi-stochastic poetry)

https://inkpi.blogspot.com/2005/05/1641b-onda-criptica.html

(+) keyword "fracture" in FonT

https://flashontrack.blogspot.com/search?q=fracture

# gst: streak-vortex instabilities in heterogeneous turbulent boundary layers

AA << re-examine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness wavelengths 0.32≤S/δ¯¯≤3.63, where S is the width of the roughness strips and δ¯¯ is the spanwise-averaged boundary-layer thickness. >>

<< The heterogeneous cases induce counter-rotating secondary flows, and these are compared to the large-scale turbulent structures that occur naturally over the smooth wall. Both appear as meandering elongated high- and low-momentum streaks in the instantaneous flow field. >>

<< Results suggest that the secondary flows might be spanwise-locked turbulent structures, with S/δ¯¯ governing the strength of the turbulent structures and possibly the efficacy of the surface in locking the structures in place (most effective when S/δ¯¯≈1). >>

<< Conditional averages of the fluctuating velocity fields of both spanwise heterogeneous and smooth wall cases result in structures that are strongly reminiscent of the streak-vortex instability model. (proposed in Jeong et al.,1997) >>

<< One outstanding question that remains unanswered in the present study is the cause of the prominent meandering of the turbulent structures, which is only observed when S/δ¯¯≈1 >>️️

️

Dea Daniella Wangsawijaya, Nicholas Hutchins. Investigation of unsteady secondary flows and large-scale turbulence in heterogeneous turbulent boundary layers. arXiv: 2110.02268v1 [physics.flu-dyn]. Oct 5, 2021.

https://arxiv.org/abs/2110.02268

keywords: gst, fluid dynamics, vortices, vortex instability, streak-vortex instability,  roughness, heterogeneous roughness, turbulence, turbulent boundary layers.

# s-gst: modulational instabilities

<< Modulational instability has been known since the 1960s. When you have small perturbations at the input, you’ll have big changes at the output >>

Now <<  it appears that (AA) have captured the essence of the phenomenon >>

http://www.buffalo.edu/news/releases/2016/02/042.html

Gino Biondini, Dionyssios Mantzavinos. Universal Nature of the Nonlinear Stage of Modulational Instability. Phys. Rev. Lett. 116, 043902 – Published 27 January 20

http://dx.doi.org/10.1103/PhysRevLett.116.043902

# gst: myriad of complex dynamics from the atomization of acoustically levitated droplets

AA << report the dynamics of a droplet levitated in a single-axis acoustic levitator. The deformation and atomization behavior of the droplet in the acoustic field exhibits a myriad of complex phenomena, in sequences of steps. These include the primary breakup of the droplet through stable levitation, deformation, sheet formation, and equatorial atomization, followed by secondary breakup which could be umbrella breakup, bag breakup, bubble breakup or multistage breakup depending on the initial size of the droplet. >>

<< Both the primary and the secondary breakup of the droplet admit interfacial instabilities such as Faraday instability, Kelvin Helmholtz (KH) instability, RT instability, and RP instability and are well described with visual evidence. >>️

Sunil K. Saroj, Rochish M. Thaokar. Atomisation of an acoustically levitated droplet: Experimental observations of a myriad of complex phenomenon. arXiv: 2307.00400v1 [physics.flu-dyn]. Jul 1, 2023.

https://arxiv.org/abs/2307.00400

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

Keywords: gst, drop, droplet, transition, instability

# gst: analogy between quasi-2D and 3D liquid drops.

<< Liquid drops are everywhere around us and important in numerous technological applications. Here, (AA) demonstrate a quasi-two-dimensional (Q2D) analogy to the regular, often close to axisymmetric, three-dimensional (3D) drops. >>️

<< The Q2D drops are created by confining liquids between vertical walls, leading to formation of low aspect ratio capillary bridges that are deformed by gravity. When stationary, the Q2D drops adopt projected shapes that are analogous to 3D sessile drops, ranging from circular drops to puddles. >>️

<< When moving, the Q2D drops exhibit capillary and fluid mechanical behaviours analogous to 3D drops, including impacts and sliding on pseudo-surfaces. The Q2D drops also exhibit considerably more complex phenomena such as levitation, instabilities and pattern formation when subjected to external electric, magnetic and flow fields -- all seen also in regular 3D drops. >>️

<< 3D-Q2D analogy suggests that the diverse and often complicated phenomena observed in 3D drops can be studied in the Q2D geometry, >>

️

Tytti Kärki, Into Pääkkönen, et al. Quasi-Two-Dimensional Drops. arXiv: 2401.11845v1 [physics.flu-dyn]. Jan 22, 2024.

https://arxiv.org/abs/2401.11845

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

Keywords: gst, drop, droplet, droploid, analogy