# gst: when a phase transition could be controlled by a fixed point of infinite disorder

AA << apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First (They) recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for arbitrary size of the block. For the model with three-spin couplings (They) calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. (AA) have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus this model represents a new infinite disorder universality class. >>️

Ferenc Iglói, Yu-Cheng Lin. Random quantum Ising model with three-spin couplings. arXiv:2503.18690v1 [cond-mat.dis-nn]. Mar 24, 2025.

https://arxiv.org/abs/2503.18690

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

Keywords: gst, disorder, order, transition

# gst: noise as endogenous control

<< Systems biology faces the monumental task of synthesizing vast amounts of molecular facts into a cohesive whole. While it is recognized that stochasticity is ubiquitous in the cell, with noise playing a role in gene expression, differentiation, and switching (..), it is still commonly argued that the cell functions in spite of the noisy cellular environment. >>️

<< Stochastic systems have a control-theoretic interpretation in which noise plays the role of endogenous control. In the weak-noise limit, relevant at low temperatures or in large populations, control is optimal and an exact mathematical mapping from noise to control is described, where the maximizing the probability of a state becomes the control objective. >>

<< In Langevin dynamics noise is identified directly with control, while in general Markov jump processes, which include chemical reaction networks and electronic circuits, (AA) use the Doi-Zel'dovich-Grassberger-Goldenfeld-Peliti path integral to identify the `response' or `tilt' field π as control, which is proportional to the noise in the semiclassical limit. This solves the longstanding problem of interpreting π. >>

AA << illustrate the mapping on multistable chemical reaction networks and systems with unstable fixed points. The noise-control mapping builds intuition for otherwise puzzling phenomena of stochastic systems: why the probability is generically a non-smooth function of state out of thermal equilibrium; why biological mechanisms can work better in the presence of noise; and how agentic behavior emerges naturally without recourse to mysticism. >>

Eric De Giuli. Noise equals endogenous control. arXiv: 2503.15670v2 [q-bio.MN]. Mar 24, 2025.

https://arxiv.org/abs/2503.15670

Also: noise, disorder & fluctuations, transition, dance, jazz, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, disorder, transition, ethno, crosstalk, gossip, misinformation, fake news, dance, jazz

# gst: dynamics of fluid-driven fractures across material heterogeneities.

<< Fracture propagation is highly sensitive to the conditions at the crack tip. In heterogeneous materials, microscale obstacles can cause propagation instabilities. Macroscopic heterogeneities modify the stress field over scales larger than the tip region. >>

 Here AA << experimentally investigate the propagation of fluid-driven fractures through multilayered materials. (They) focus on analyzing fracture profiles formed upon injection of a low-viscosity fluid into a two-layer hydrogel block. >>

<< Experimental observations highlight the influence of the originating layer on fracture dynamics. Fractures that form in the softer layer are confined, with no penetration in the stiffer layer. Conversely, fractures initiated within the stiffer layer experience rapid fluid transfer into the softer layer when reaching the interface. >>

AA << report the propagation dynamics and show that it is controlled by the toughness contrast between neighboring layers, which drives fluid flow. (They) model the coupling between elastic deformation, material toughness, and volume conservation. After a short transient regime, scaling arguments capture the dependence of the fracture geometry on material properties, injection parameters, and time. These results show that stiffness contrast can modify fracture propagation over large length scales and demonstrate the importance of macroscopic scale heterogeneities on fracture dynamics. >>

Sri Savya Tanikella, Marie C. Sigallon, Emilie Dressaire. Dynamics of fluid-driven fractures across material heterogeneities. Phys. Rev. E 111, 025504. Feb 28, 2025.   https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.025504     arXiv: 2407.10298v1 [physics.flu-dyn]. Jul 14, 2024.  https://arxiv.org/abs/2407.10298

Also: fracture, crack, elastic, 

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

Keywords: gst, fracture, crack, elasticity, instability, disorder, transitions

# gst: emergent flocking in mixtures of antialigning self-propelled particles.

FIG. 4. (c) Mean field phase diagram with disorder (green triangles), polarized moving bands (blue circles), and polarized patches (orange squares).

AA << observe a flocking mechanism, the emergence of a state with global polar order, in mixed systems of self-propelled particles with purely antialigning interactions, i.e., the ground state for any pair of particles is to be opposedly oriented. In binary mixtures, (They) find that flocking can be realized by cross-species antialigning that is dominant compared to intraspecies antialignment. >>

<< While the key mechanism can be understood within a mean-field description, beyond mean-field (AA) develop an asymptotically exact Boltzmann-scattering theory from first principles.  This theory yields analytical predictions for the flocking transition and shows excellent quantitative agreement with simulations of dilute systems. For large systems, (They) find either microphase separation or static patterns with patches or stripes that carry different polarization orientations. >>️

Rüdiger Kürsten, Jakob Mihatsch, Thomas Ihle. Emergent flocking in mixtures of antialigning self-propelled particles. Phys. Rev. E 111, L023402. Feb 21, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.L023402

Also: particle, flock, flocking, swarm, order, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, self-propelled particles, flock, flocking, swarm, order, disorder, transitions

# gst: when homogeneous systems meet dissipation and disorder.

AA << investigate the localization and topological properties of the non-equilibrium steady state (NESS) in a one-dimensional homogeneous system. (Their) results demonstrate that, despite the absence of disorder in the initial system, the NESS can exhibit localization under bond dissipation. >>

<< Conversely, for an initially flat-band system with compactly localized wave functions, the NESS is delocalized. >>

<< Furthermore, (They) find that the initial localization characteristics of the system significantly influence the localization properties of the NESS. Drawing upon the concept of Bose-Einstein condensate broadening in cold-atom experiments, along with experimental data, (AA) systematically characterize the impact of disorder on the localization and topological properties of the NESS. >>

<< The phase diagram reveals that the NESS can be topologically non-trivial even when the initial state is topologically trivial, and that the topological triviality of the initial state weakens the topological non-triviality of the NESS. >>

Xixi Feng, Ao Zhou, et al. When Homogeneous Systems Meet Dissipation and Disorder. arXiv: 2502.11383v1 [cond-mat.dis-nn]. Feb 17, 2025. 

https://arxiv.org/abs/2502.11383

Also: order, disorder, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, transitions

# gst: order and chaos in systems of coaxial vortex pairs

Fig. B.12: Ex. with 4 interact. vortex pairs

AA << have analyzed interactions between two and three coaxial vortex pairs, classifying their dynamics as either ordered or chaotic based on strengths, initial sizes, and initial horizontal separations.  >>️

They << found that periodic cases are scattered among chaotic ones across different initial configurations. Quasi-periodic leapfrogging typically occurs when the initial distances between the vortex pairs are small and cannot coexist with vortex-pair overtake. When the initial configuration splits into two interacting vortex pairs and a single propagating vortex pair, the two interacting pairs consistently exhibit periodic leapfrogging. For the smallest initial horizontal separations, the system predominantly exhibits chaotic or quasi-periodic motions rather than periodic leapfrogging with a single frequency. This behavior is due to the strong coupling between all three vortex pairs. When the pairs are in close proximity, more complex and chaotic dynamics emerge instead of periodic motion. >>

Their << findings indicate that quasi-periodic leapfrogging and chaotic interactions generally occur when the three vortex pairs have similar strengths and initial sizes. Conversely, discrepancies in these parameters cause the system to disintegrate into two subsystems: a single propagating vortex pair and two periodically leapfrogging pairs. >>️

️

Christiana Mavroyiakoumou, Wenzheng Shi. Order and Chaos in Systems of Coaxial Vortex Pairs. arXiv: 2502.07002v1 [physics.flu-dyn]. Feb 10, 2025. ️

https://arxiv.org/abs/2502.07002

Also: chaos, vortex, order, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, vortex, order, disorder, disorder & fluctuations

# gst: intrinsic disorder bars intruders (from biomolecular condensates)

<< It was recently discovered that eukaryotic cells are host to a multiplicity of biomolecular condensates. These condensates typically contain protein and/or RNA components with intrinsically disordered regions (IDRs). While IDRs have been proposed and demonstrated to play many roles in condensate biology, (AA) suggest here an additional crucial role of IDRs, which is to exclude unwanted “intruders” from condensates. This exclusion effect arises from the large conformational entropy of IDRs; i.e., there is a high free-energy cost to occupying space that would otherwise be available to the IDRs. By combining polymer theory with sticker-spacer simulations, (They) show that the relevant insertion free energy increases with the concentration of IDRs in the condensate as well as with intruder size, attaining a linear scaling with surface area for large intruders. >>

AA << find that at realistic IDR concentrations, particles as small as the size of an average protein (4 nm in diameter) can be 97% excluded from condensates. To overcome this entropic barrier, molecules must interact favorably with condensate components to be recruited as clients. Application of the developed size-exclusion theory to biological condensates suggests that condensate IDRs may play a generic exclusionary role across organisms and types of condensates. >>️

Vladimir Grigorev, Ned S. Wingreen, Yaojun Zhang. Conformational Entropy of Intrinsically Disordered Proteins Bars Intruders from Biomolecular Condensates. PRX Life 3, 013011. Feb 14, 2025.

https://journals.aps.org/prxlife/abstract/10.1103/PRXLife.3.013011

Also: order, disorder, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, transitions

# gst: necklacelike pattern of vortex bound states

<< A vortex is a topological defect in the superconducting condensate when a magnetic field is applied to a type-II superconductor, (..). Because of the confinement of the quasiparticles by a vortex, it exhibits a circular-shaped pattern of bound states with discrete energy levels, (..) >>

 Here, AA << report a completely new type of vortex pattern which is necklacelike in an iron-based superconductor (..). (AA) theoretical analysis shows that this necklacelike vortex pattern arises primarily from selective off-shell interference between vortex bound states of opposite angular momenta in the presence of rotational symmetry breaking due to disorders. >>

<< This fascinating effect can be observed in a system with a small Fermi energy and wave vector, conditions fortuitously met in (Their) samples. (AA) results not only disclose a novel vortex structure, but also unravel a completely new quantum phenomenon in the superconducting condensate. >>️

Zhiyong Hou, Kailun Chen, et al. Necklacelike Pattern of Vortex Bound States. Phys. Rev. X 15, 011027. Feb 7, 2025.   https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011027   arXiv: 2407.08547v1 [cond-mat.supr-con]. Jul 11, 2024.    https://arxiv.org/abs/2407.08547

Also: vortex, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, vortex bound states, symmetry breaking, disorder, disorder & fluctuations, necklacelike patterns

# gst: apropos of subdiffusive behaviors, the boomerang effect in classical stochastic models.

<< The phenomenon of Anderson localization, occurring in a disordered medium, significantly influences the dynamics of quantum particles. A fascinating manifestation of this is the “quantum boomerang effect” (QBE), observed when a quantum particle, propelled with a finite initial velocity, reverses its average trajectory, eventually halting at its starting point. >>

AA << uncover evidence of a similar effect in classical systems, characterized by the absence of typical diffusion processes. (Their) investigation encompasses both simplified probabilistic models and more complex phenomenological models that link classical with quantum mechanics. The results indicate that the boomerang effect is not confined to the quantum realm and may also be present in diverse systems exhibiting subdiffusive behavior. >>️

Santiago Zamora, Lisan M. M. Durao, et al. Boomerang effect in classical stochastic models. Phys. Rev. E 111, 024104. Feb 3, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.024104 

Also: behav, particle, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, behavior, particles, disorder, disorder & fluctuations, stocasticity, boomerang effect

# gst: criticality and multistability in quasi-2D turbulence

       Fig. 1(a) Helmholtz resonators

<< Two-dimensional (2D) turbulence, despite being an idealization of real flows, is of fundamental interest as a model of the spontaneous emergence of order from chaotic flows. The emergence of order often displays critical behavior, whose study is hindered by the long spatial and temporal scales involved. >>

Here AA << experimentally study turbulence in periodically driven nanofluidic channels with a high aspect ratio using superfluid helium. (They) find a multistable transition behavior resulting from cascading bifurcations of large-scale vorticity and critical behavior at the transition to quasi-2D turbulence consistent with phase transitions in periodically driven many-body systems. >>

AA << demonstrate that quasi-2D turbulent systems can undergo an abrupt change in response to a small change in a control parameter, consistent with predictions for large-scale atmospheric or oceanic flows. >>️

Filip Novotny, Marek Talir, et al. Critical behavior and multistability in quasi-two-dimensional turbulence. arXiv: 2406.08566v1 [physics.flu-dyn]. Jun 12, 2024.

https://arxiv.org/abs/2406.08566

Also: order, disorder, disorder & fluctuations, turbulence, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, criticality, turbulence, transition 

# gst: soliton dynamics over a disordered topography

AA << report on the dynamics of a soliton propagating on the surface of a fluid in a 4-m-long canal with a random or periodic bottom topography. Using a full space-and-time resolved wave field measurement, (They) evidence, for the first time experimentally, how the soliton is affected by the disorder, in the context of Anderson localization, and how localization depends on nonlinearity. >>

<< For weak soliton amplitudes, the localization length is found in quantitative agreement with a linear shallow-water theory. For higher amplitudes, this spatial attenuation of the soliton amplitude is found to be enhanced. >>

<< Behind the leading soliton slowed down by the topography, different experimentally unreported dynamics occur: fission into backward and forward nondispersive pulses for the periodic case, and scattering into dispersive waves for the random case. >>

Guillaume Ricard, Eric Falcon. Soliton Dynamics over a Disordered Topography. Phys. Rev. Lett. 133, 264002. Dec 27, 2024.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.264002

Also: soliton, waves, disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, soliton, waves, disorder

# 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: 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: when generalized diffusion could result from stochastic processes.

<< Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach of a generalization that incorporates heterogeneities in either the tracers or the environment. >>

AA present << a modification of Lévy's representation of fBm for the case in which the generalized diffusion coefficient is a stochastic process. (They) derive analytical expressions for the autocovariance function and both ensemble- and time-averaged mean squared displacements. Further, (AA)  validate the efficacy of the developed framework in two-state systems, comparing analytical asymptotic expressions with numerical simulations. >>️

Adrian Pacheco-Pozo, Diego Krapf. Fractional Brownian motion with fluctuating diffusivities. Phys. Rev. E 110, 014105. Jul 1, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.014105

Also: disorder, fluctuations, network, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, fractional Brownian motion, fBm, Lévy, disorder, fluctuations, anomalous, network, transition

# gst: chaos controlled and disorder driven phase transitions by breaking permutation symmetry

<< Introducing disorder in a system typically breaks symmetries and can introduce dramatic changes in its properties such as localization. At the same time, the clean system can have distinct many-body features depending on how chaotic it is. >>

<< In this work the effect of permutation symmetry breaking by disorder is studied in a system which has a controllable and deterministic regular to chaotic transition. >>

<< Results indicate a continuous phase transition from an area-law to a volume-law entangled phase irrespective of whether there is chaos or not, as the strength of the disorder is increased. The critical disorder strength obtained by finite size scaling, indicate a strong dependence on whether the clean system is regular or chaotic to begin with. >>

<< Additionally, (AA) find that a relatively small disorder is seen to be sufficient to delocalize a chaotic system. >>

Manju C, Arul Lakshminarayan, Uma Divakaran. Chaos controlled and disorder driven phase transitions by breaking permutation symmetry. arXiv: 2406.00521v1 [quant-ph]. Jun 1, 2024. 

https://arxiv.org/abs/2406.00521

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

Keywords: gst, transition, chaos, disorder 

FonT: who is Manju C?

# gst: inertia onset in disordered porous media flow.

AA << investigate the very onset of the inertial regime in pore-scale fluid flow in a three-dimensional, disordered porous media. >>️

Their << analysis shows that the onset of inertia observed in a standard way by computing the friction factor appears at a Reynolds number two orders of magnitude higher than indicated by analyzing tortuosity and spatial distribution of kinetic energy. >>️

Damian Sniezek, Sahrish B. Naqvi, Maciej Matyka. Inertia onset in disordered porous media flow. arXiv: 2403.00456v2 [physics.flu-dyn]. Mar 26, 2024. 

https://arxiv.org/abs/2403.00456

Also: inertia, disorder, in FonT 

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

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

Keywords: gst, inertia, disorder

# gst: an analogy between geometrical frustrations and nonreciprocal systems

<< A system is geometrically frustrated when its members cannot find a configuration that simultaneously minimizes all their interaction energies, (..). A nonreciprocal system is one whose members have conflicting, asymmetric goals, as exemplified by an ecosystem of predators and prey. >>️

<< Ryo Hanai (..) has identified a powerful mathematical analogy between those two types of dynamical systems. >>️

Peter Littlewood. Nonreciprocal Frustration Meets Geometrical Frustration. Physics 17, 32. Feb 26, 2024. 

https://physics.aps.org/articles/v17/32

Ryo Hanai. Nonreciprocal Frustration: Time Crystalline Order-by-Disorder Phenomenon and a Spin-Glass-like State. Phys. Rev. X 14, 011029. Feb 26, 2024. 

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.011029

Also: order, disorder, disorder & fluctuations, noise, analogy, in https://www.inkgmr.net/kwrds.html

Keywords: gst, analogy, order, disorder, noise

# life: it’s time to admit that ...

<< For too long, scientists have been content in espousing the lazy metaphor of living systems operating simply like machines, (..) Yet, it’s important to be open about the complexity of biology — including what we don’t know — because public understanding affects policy, health care and trust in science.  “So long as we insist that cells are computers and genes are their code,” writes Ball, life might as well be “sprinkled with invisible magic”. But, reality “is far more interesting and wonderful”, as he explains in this must-read user’s guide for biologists and non-biologists alike. >>️

Denis Noble. It’s time to admit that genes are not the blueprint for life. Nature. 626, 254-255 (2024). Feb 5,  2024. 

https://www.nature.com/articles/d41586-024-00327-x

Philip Ball. How Life Works: A User’s Guide to the New Biology. Pan Macmillan (2024). 

https://www.panmacmillan.com/authors/philip-ball/42387

Also: disorder, disorder & fluctuation, in https://www.inkgmr.net/kwrds.html  

Keywords: life, disorder, fluctuations

FonT: this point of view, published in the 70s-80s, would have made a damned impression. 

# gst: transitions in disordered medium.

AA << study computationally the dynamics of forced, Brownian particles through a disordered system. As the concentration of mobile particles and/or fixed obstacles increase, (AA) characterize the different regimes of flow and address how clogging develops. >>️

AA << show that clogging is preceded by a wide region of anomalous transport, characterized by a power law decay of intermittent bursts. (..) this abnormal flow region is characterized by a coexistence between mobile and arrested particles, and their relative populations change smoothly as clogging is approached. >>

️

Sergi G. Leyva, Ignacio Pagonabarraga. Clogging transition and anomalous transport in driven suspensions in a disordered medium. Phys. Rev. E 109, 014618. Jan 31, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.014618

img:  https://twitter.com/PhysRevE/status/1753068208586711072   

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

Keywords: gst, transition, particle, disorder

# gst: intertwining order, disorder, and hierarchy

<< Nature hosts a wealth of materials showcasing intricate structures intertwining order, disorder, and hierarchy, delivering resilient multifunctionality surpassing perfect crystals or simplistic disordered materials. The engineering of such materials through nanoparticle assembly represents a burgeoning field, poised with potential to yield sustainable material systems rivaling or exceeding biological functionalities. >>

AA << review delineates the fundamental concept of complexity in the context of nanoscale materials. >>

Xiaoming Mao, Nicholas Kotov. Complexity, Disorder, and Functionality of Nanoscale Materials. arXiv: 2401.09567v1 [cond-mat.soft]. Jan 17, 2024. 

https://arxiv.org/abs/2401.09567

Also: nano, particle, order, disorder, in  https://www.inkgmr.net/kwrds.html

Keywords: nano, particle, order, disorder