Macroscopic Order Research Articles

Emergent order in epithelial sheets by interplay of cell divisions and cell fate regulation.

The fate choices of stem cells between self-renewal and differentiation are often tightly regulated by juxtacrine (cell-cell contact) signalling. Here, we assess how the interplay between cell division, cell fate choices, and juxtacrine signalling can affect the macroscopic ordering of cell types in self-renewing epithelial sheets, by studying a simple spatial cell fate model with cells being arranged on a 2D lattice. We show in this model that if cells commit to their fate directly upon cell division, macroscopic patches of cells of the same type emerge, if at least a small proportion of divisions are symmetric, except if signalling interactions are laterally inhibiting. In contrast, if cells are first 'licensed' to differentiate, yet retaining the possibility to return to their naive state, macroscopic order only emerges if the signalling strength exceeds a critical threshold: if then the signalling interactions are laterally inducing, macroscopic patches emerge as well. Lateral inhibition, on the other hand, can in that case generate periodic patterns of alternating cell types (checkerboard pattern), yet only if the proportion of symmetric divisions is sufficiently low. These results can be understood theoretically by an analogy to phase transitions in spin systems known from statistical physics.

Higher-order interaction induced chimeralike state in a bipartite network.

We report higher-order coupling induced stable chimeralike state in a bipartite network of coupled phase oscillators without any time-delay in the coupling. We show that the higher-order interaction breaks the symmetry of the homogeneous synchronized state to facilitate the manifestation of symmetry breaking chimeralike state. In particular, such symmetry breaking manifests only when the pairwise interaction is attractive and higher-order interaction is repulsive, and vice versa. Further, we also demonstrate the increased degree of heterogeneity promotes homogeneous symmetric states in the phase diagram by suppressing the asymmetric chimeralike state. We deduce the low-dimensional evolution equationsfor the macroscopic order parameters using Ott-Antonsen ansatz and obtain the bifurcation curves from them using the software xppaut, which agrees very well with the simulation results. We also deduce the analytical stability conditions for the incoherent state, in-phase and out-of-phase synchronized states, which match with the bifurcation curves.

Directional cues affect the collective behaviour of self-propelled particles in one dimension

This study explores the effect of quenched disorder on the characteristics of self-propelled particles in one dimension. Here, particles interact with disorder which serve as directional cues. The study investigates how the density of the directional cues influences the emergence of ordering and clustering in the collection of the self-propelled particles. We introduce the microscopic model as well as corresponding coarse-grained equations of motion for the local density and the orientation of particles. Directional cues affect the macroscopic ordering in the system, the size of the ordered clusters decays algebraically with density of cues. Further, in the presence of directional cues, a big macroscopic cluster breaks into small clusters, leading to the localization of particles around it and resulting in high density around the cues.

Molecules as Lubricants at the Nanoscale:Tunable Growth of Organic Structures from Nano- to Millimeter-Scale Using Solvent Vapour Annealing.

The creation of ordered structures of molecules assembled from solution onto a substrate is a fundamental technological necessity across various disciplines, spanning from crystallography to organic electronics. However, achieving macroscopic order poses significant challenges, since the process of deposition is inherently impacted by factors like solvent evaporation and dewetting flows, which hinder the formation of well-organized structures. Traditional methods like drop casting or spin coating encounter limitations due to the rapid kinetics of solvent evaporation, leading to limited control over final uniformity and order. In response to these challenges, Solvent Vapour Annealing (SVA) has emerged as a promising solution for realizing ordered molecular structures at scales ranging from nano- to milli- meters. SVA decouples the self-assembly stage from the deposition stage by utilizing solvent vapours which can enable rearrangement, movement, and diffusion of large molecules on the surface even on a macroscopic scale. Essentially acting as "molecular lubricants," solvent vapours enable the formation of well-ordered molecular films. This review discusses the advancements, obstacles, and promising strategies associated with utilizing SVA for the development of innovative nanostructured thin films, and emphasizes the originality and effectiveness of molecular assembly on substrates achieved through this approach.

Spontaneous piezoeletric effect as evidence of ferroelastoelectricity in guanidine zinc sulfate crystal

The crystal of [C(NH2)3]2Zn(SO4)2 guanidine zinc sulfate was grown and its structure, dilatometric, dielectric, elastic and piezoelectric properties were studied in a broad temperature range, covering the phase transition point. The crystal undergoes a continuous phase transition at 178 K from the room temperature tetragonal phase with a space group I4¯2d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{I}\\overline{4}2\ ext{d }$$\\end{document} to the tetragonal low temperature phase with a space group I4¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{I}\\overline{4 }$$\\end{document}. The structural X-ray studies allowed proposing molecular mechanism associated with the rearrangement in the configuration of N–H⋯O hydrogen bonds and reorientation of guanidine cations in the structure, leading to a change in the symmetry of the low temperature phase. Results of thermal expansion and dielectric studies are typical of a structural nonferroelectric continuous transition. Also measurement of piezoelectric and elastic properties revealed small anomalies at 178 K. Below the transition temperature, a new piezoelectric component, that is a ferroelastoelectric macroscopic order parameter, was found.

Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it.

We introduce and investigate the effects of a new class of stochastic resetting protocol called subsystem resetting, whereby a subset of the system constituents in a many-body interacting system undergoes bare evolution interspersed with simultaneous resets at random times, while the remaining constituents evolve solely under the bare dynamics. Here, by reset is meant a reinitialization of the dynamics from a given state. We pursue our investigation within the ambit of the well-known Kuramoto model of coupled phase-only oscillators of distributed natural frequencies. Here, the reset protocol corresponds to a chosen set of oscillators being reset to a synchronized state at random times. We find that the mean ω_{0} of the natural frequencies plays a defining role in determining the long-time state of the system. For ω_{0}=0, the system reaches a synchronized stationary state at long times, characterized by a time-independent nonzero value of the synchronization order parameter that quantifies macroscopic order in the system. Moreover, we find that resetting even an infinitesimal fraction of the total number of oscillators, in the extreme limit of infinite resetting rate, has the drastic effect of synchronizing the entire system, even in parameter regimes in which the bare evolution does not support global synchrony. By contrast, for ω_{0}≠0, the dynamics allows at long times either a synchronized stationary state or an oscillatory synchronized state, with the latter characterized by an oscillatory behavior as a function of time of the order parameter, with a nonzero time-independent time average. Our results thus imply that the nonreset subsystem always gets synchronized at long times through the act of resetting of the reset subsystem. Our results, analytical using the Ott-Antonsen ansatz as well as those based on numerical simulations, are obtained for two representative oscillator frequency distributions, namely, a Lorentzian and a Gaussian. Given that it is easier to reset a fraction of the system constituents than the entire system, we discuss how subsystem resetting may be employed as an efficient mechanism to control attainment of global synchrony in the Kuramoto system.

Facile synthesis and magneto-alignment effect on the microwave absorption property of NiCo2O4/NiO/Co3O4 composites

A simple method of high-temperature ignition to metalorganics was successfully used to synthesise composites of NiCo2O4, NiO and Co3O4. A detailed investigation of the composite’s microwave absorption properties revealed the magneto-alignment effect. By closely arranging NiCo2O4, NiO and Co3O4 nano-particles in epoxy resin, the magnetic exchange is strengthened under the influence of a magnetic field. The sample without magnetic alignment, S0, exhibited poor absorption efficiency with reflection loss (RL) values hardly reaching − 10 dB across a frequency range of fixed and different thicknesses (2–18 GHz). In comparison, the oriented composite exhibited higher permittivity and permeability, particularly in the high-frequency range. Considering the improved impedance matching and reasonable adjustment of dielectric and magnetic losses, the microwave absorbing performance of the oriented composite substantially improved in the 10–14 GHz range. The minimum RL is reduced to − 45.11 dB with an effective bandwidth of 4 GHz. Herein, we present a straightforward method to increase the microwave absorption performance of NiCo2O4 by modifying the macroscopic order and degree.

Effect of higher-order interactions on chimera states in two populations of Kuramoto oscillators.

We investigate the effect of the fraction of pairwise and higher-order interactions on the emergent dynamics of the two populations of globally coupled Kuramoto oscillators with phase-lag parameters. We find that the stable chimera exists between saddle-node and Hopf bifurcations, while the breathing chimera lives between Hopf and homoclinic bifurcations in the two-parameter phase diagrams. The higher-order interaction facilitates the onset of the bifurcation transitions at a much lower disparity between the inter- and intra-population coupling strengths. Furthermore, the higher-order interaction facilitates the spread of breathing chimera in a large region of the parameter space while suppressing the spread of the stable chimera. A low degree of heterogeneity among the phase-lag parameters promotes the spread of both stable chimera and breathing chimera to a large region of the parameter space for a large fraction of the higher-order coupling. In contrast, a large degree of heterogeneity is found to decrease the spread of both chimera states for a large fraction of the higher-order coupling. A global synchronized state is observed above a critical value of heterogeneity among the phase-lag parameters. We have deduced the low-dimensional evolution equations for the macroscopic order parameters using the Ott-Antonsen Ansatz. We have also deduced the analytical saddle-node and Hopf bifurcation curves from the evolution equations for the macroscopic order parameters and found them to match with the bifurcation curves obtained using the software XPPAUT and with the simulation results.

Ion transport induced room-temperature insulator-metal transition in single-crystalline Cu2Se.

Cu2Se is a superionic conductor above 414 K, with ionic conductivities reaching that of molten salts. The superionic behavior results from hopping Cu ions between different crystallographic sites within the Se scaffold. However, the properties of Cu2Se below 414 K are far less known due to experimental limitations imposed by the bulk or polycrystalline samples that have been available so far. Here, we report the synthesis of ultra-thin, large-area single crystalline Cu2Se samples using a chemical vapor deposition method. The as-synthesized Cu2Se crystals exhibit optically and electrically detectable and controllable robust phases at room temperature and above. We demonstrate that Cu ion vacancies can be manipulated to induce an insulator-metal transition, which exhibits 6 orders of magnitude change in the electrical resistance of two terminal devices, accompanied by an optical change in the phase configuration. Our experiments show that the high mobility of the liquid-like Cu ion vacancies in Cu2Se causes macroscopic ordering in the Cu vacancies. Consequently, phase distribution over the crystals is not dictated by the diffusive motion of the ions but by the local energy minima formed due to the phase transition. As a result, long-range vacancy ordering of the crystal below 414 K becomes optically observable at a micrometer scale. This work demonstrates that Cu2Se could be a prototypical system where long-range ordering properties can be studied via electrical and optical methods.

Berry-Curvature Engineering for Nonreciprocal Directional Dichroism in Two-Dimensional Antiferromagnets.

In two-dimensional antiferromagnets, we find that the mixed Berry curvature can be attributed as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption between opposite propagation directions. This Berry curvature is closely related to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and strength can be tuned via strain direction. We choose the lattice model of MnBi_{2}Te_{4} as a concrete example. The coupling between mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, which is distinct from the multiferroic order P×M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way for the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Mesostructured Materials with Controllable Long-Range Orientational Ordering and Anisotropic Properties.

Inorganic-organic mesophase materials provide a wide range of tunable properties, which are often highly dependent on their nano-, micro-, or meso-scale compositions and structures. Among these are macroscopic orientational order and corresponding anisotropic material properties, the adjustability of which are difficult to achieve. This is due to the complicated transient and coupled transport, chemical reaction, and surface processes that occur during material syntheses. By understanding such processes, general criteria are established and used to prepare diverse mesostructured materials with highly aligned channels with uniform nanometer dimensions and controllable directionalities over macroscopic dimensions and thicknesses. This is achieved by using a micropatterned semipermeable poly(dimethylsiloxane) stamp to manage the rates, directions, and surfaces at which self-assembling phases nucleate and the directions that they grow. This enables mesostructured surfactant-directed silica and titania composites, including with functional guest species, and mesoporous carbons to be prepared with high degrees of hexagonal order, as well as controllable orthogonal macroscopic orientational order. The resulting materials exhibit novel anisotropic properties, as demonstrated by the example of direction-dependent photocurrent generation, and are promising for enhancing the functionality of inorganic-organic nanocomposite materials in separations, catalysis, and energy conversion applications.

Diverse phase transitions in Kuramoto model with adaptive mean-field coupling breaking the rotational symmetry

We consider the paradigmatic Kuramoto oscillators coupled via an adaptive mean-field variable that breaks the rotational symmetry. The evolution equation for the mean-field variable is governed by the linear ordinary differential equation corresponding to a low-pass filter with a time-scale parameter, which attenuates the mean-field signal by filtering its high frequency components. We find distinct phase transitions among the incoherent state, standing wave state and synchronized stationary state in both forward and reverse traces in the entire range of the time-scale parameter. In particular, one can observe two distinct continuous transitions, a continuous transition followed by a discontinuous transition, or a single discontinuous transition among the distinct dynamical states in the forward trace depending on the range of the time-scale parameter, which determines the degree of attenuation. Further, one can also observe two distinct continuous transitions or a single discontinuous desynchronization transition in the reverse trace depending on the time-scale parameter. We derive the evolution equations for the macroscopic order parameters governing the dynamics of the discrete set of coupled phase oscillators. We also deduce the analytical conditions for the stability of the Hopf, pitchfork and saddle–node bifurcations, and find them to be in consistent with the dynamical transitions observed using the simulation.

Effect of quantum dots on the phase behavior and order of 8CB liquid crystal

We experimentally investigate the impact of surface functionalized hydrophobic core-shell CdSe/ZnS quantum dots on the phase behavior and order of the host liquid crystal compound 4-cyano-4'-octylbiphenyl (8CB) by means of polarized optical microscopy, polarized micro-Raman spectroscopy and X-ray diffraction. The orientational order of the nanocomposite system is probed by means of birefringence measurements as a function of temperature and mass fraction of the quantum dots. The dispersion quality of the dopant in the samples, partial-aggregation phenomena and/or nanoparticle organization give rise to non-monotonic variation of the probed thermodynamic quantities. A critical dopant mass fraction above which the nematic phase becomes paranematic is evidenced. A phenomenological model accounts for phase separation effects and a qualitative interpretation of the experimental results. The impact of nanoparticles on the macroscopic nematic order is discussed in the frame of a random anisotropy Lebwohl-Lasher model.

Improved Route to Linear Triblock Copolymers by Coupling with Glycidyl Ether-Activated Poly(ethylene oxide) Chains.

Poly(ethylene oxide) block copolymers (PEOz BCP) have been demonstrated to exhibit remarkably high lithium ion (Li+) conductivity for Li+ batteries applications. For linear poly(isoprene)-b-poly(styrene)-b-poly(ethylene oxide) triblock copolymers (PIxPSyPEOz), a pronounced maximum ion conductivity was reported for short PEOz molecular weights around 2 kg mol-1. To later enable a systematic exploration of the influence of the PIx and PSy block lengths and related morphologies on the ion conductivity, a synthetic method is needed where the short PEOz block length can be kept constant, while the PIx and PSy block lengths could be systematically and independently varied. Here, we introduce a glycidyl ether route that allows covalent attachment of pre-synthesized glycidyl-end functionalized PEOz chains to terminate PIxPSy BCPs. The attachment proceeds to full conversion in a simplified and reproducible one-pot polymerization such that PIxPSyPEOz with narrow chain length distribution and a fixed PEOz block length of z = 1.9 kg mol-1 and a Đ = 1.03 are obtained. The successful quantitative end group modification of the PEOz block was verified by nuclear magnetic resonance (NMR) spectroscopy, gel permeation chromatography (GPC) and differential scanning calorimetry (DSC). We demonstrate further that with a controlled casting process, ordered microphases with macroscopic long-range directional order can be fabricated, as demonstrated by small-angle X-ray scattering (SAXS), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It has already been shown in a patent, published by us, that BCPs from the synthesis method presented here exhibit comparable or even higher ionic conductivities than those previously published. Therefore, this PEOz BCP system is ideally suitable to relate BCP morphology, order and orientation to macroscopic Li+ conductivity in Li+ batteries.

A conservative phase‐field lattice Boltzmann method for incompressible two‐phase flows

AbstractIn this work, a conservative phase‐field lattice Boltzmann method (LBM) is proposed for incompressible two‐phase flows. In this method, two LB models are adopted to solve the nonlocal Allen–Cahn equation (ACE) and the Navier–Stokes equations, respectively. Unlike the previous models for the nonlocal ACE with a space‐time‐dependent Lagrange multiplier, a simple multiple‐relaxation time LB model is designed for the conservative and nonlocal ACE with a curvature‐dependent Lagrange multiplier, which can eliminate the problem of inherent coarsening process. Through the Chapman–Enskog analysis, the present LB model can correctly recover the ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LBM is validated by two tests, that is, the horizontal translation of two circular interfaces and a bubble rising under gravity, and the results show that the present LBM has a superior performance in capturing the large topological changes and small features of interfaces.

Improved hybrid Allen-Cahn phase-field-based lattice Boltzmann method for incompressible two-phase flows.

In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation(ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.

Abrupt symmetry-preserving transition from the chimera state.

We consider two populations of the globally coupled Sakaguchi-Kuramoto model with the same intra- and interpopulations coupling strengths. The oscillators constituting the intrapopulation are identical whereas the interpopulations are nonidentical with a frequency mismatch. The asymmetry parameters ensure the permutation symmetry among the oscillators constituting the intrapopulation and a reflection symmetry among the oscillators constituting the interpopulation. We show that the chimera state manifests by spontaneously breaking the reflection symmetry and also exists in almost in the entire explored range of the asymmetry parameter without restricting to the near π/2 values of it. The saddle-node bifurcation mediates the abrupt transition from the symmetry breaking chimera state to the symmetry-preserving synchronized oscillatory state in the reverse trace, whereas the homoclinic bifurcation mediates the transition from the synchronized oscillatory state to synchronized steady state in the forward trace. We deduce the governing equationsof motion for the macroscopic order parameters employing the finite-dimensional reduction by Watanabe and Strogatz. The analytical saddle-node and homoclinic bifurcation conditions agree well with the simulations results and the bifurcation curves.

Solving 2D and 3D Lattice Models of Correlated Fermions—Combining Matrix Product States with Mean-Field Theory

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature Tc for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work, we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: two- and three-dimensional materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute Tc for superconductivity in 3D arrays of weakly coupled, doped, and repulsive Hubbard ladders. The MPS+MF framework thus enables the quantitative study of USC and high-Tc superconductivity—and potentially many more correlated phases—in fermionic Q1D systems based directly on their microscopic parameters, in ways inaccessible to previous methods. This approach further allows one to treat competing macroscopic orders, such as superconducting and insulating ones, on an equal footing. Benchmarks of the framework using auxiliary-field quantum Monte Carlo techniques show that the overestimation of, e.g., Tc due to its mean-field component, is near constant in microscopic parameters. These features of the MPS+MF approach to correlated fermions open up the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.13 MoreReceived 8 July 2022Revised 7 December 2022Accepted 3 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011039Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFermionsSuperconductivityPhysical Systems3-dimensional systemsStrongly correlated systemsUnconventional superconductorsTechniquesBosonizationDensity matrix renormalization groupMean field theoryCondensed Matter, Materials & Applied Physics

Stability of line-node semimetals with strong Coulomb interactions and properties of the symmetry-broken state

We study the stability and phenomenology of line-node semimetals in the presence of Coulomb interactions. Our results indicate a phase transition to a chiral insulating state that occurs at a finite interaction threshold, which we determine. We also compute the Landau levels for out-of-plane and in-plane magnetic fields in the symmetric and symmetry-broken phases. We find that the magnetic field couples to the chiral order parameter, implying that this degree of freedom can be manipulated in situ in experiments. Finally, we check the existence of edge states in the symmetry-broken phase. On the system's boundary, we note that the metallic ``drum-head'' states that exist in the symmetric phase are gapped out. However, the symmetry-broken phase permits topological defects in the macroscopic order parameter in the form of domain walls, which host metallic ``interface states.'' These consist of linelike gap-closings that occur on the two-dimensional interfaces.

Enabling Room-Temperature Triferroic Coupling in Dual Transition-Metal Dichalcogenide Monolayers Via Electronic Asymmetry.

Triferroic compounds are the ideal platform for multistate information devices but are rare in the two-dimensional (2D) form, and none of them can maintain macroscopic order at room temperature. Herein, we propose a general strategy for achieving 2D triferroicity by imposing electric polarization into a ferroelastic magnet. Accordingly, dual transition-metal dichalcogenides, for example, 1T'-CrCoS4, are demonstrated to display room-temperature triferroicity. The magnetic order of 1T'-CrCoS4 undergoes a magnetic transition during the ferroic switching, indicating robust triferroic magnetoelectric coupling. In addition, the negative out-of-plane piezoelectricity and strain-tunable magnetic anisotropy make the 1T'-CrCoS4 monolayer a strong candidate for practical applications. Following the proposed scheme, a new class of 2D room-temperature triferroic materials is introduced, providing a promising platform for advanced spintronics.