Phase Transition Threshold Research Articles

Realizing Exceptional Points by Floquet Dissipative Couplings in Thermal Atoms.

Exceptional degeneracies and generically complex spectra of non-Hermitian systems are at the heart of numerous phenomena absent in the Hermitian realm. Recently, it was suggested that Floquet dissipative coupling in the space-time domain may provide a novel mechanism to drive intriguing spectral topology with no static analogs, though its experimental investigation in quantum systems remains elusive. We demonstrate such Floquet dissipative coupling in an ensemble of thermal atoms interacting with two spatially separated optical beams, and observe an anomalous anti-parity-time symmetry phase transition at an exception point far from the phase-transition threshold of the static counterpart. Our protocol sets the stage for Floquet engineering of non-Hermitian topological spectra, and for engineering new quantum phases that cannot exist in static systems.

Percolation Transitions in Edge-Coupled Interdependent Networks with Reinforced Inter-Layer Links.

Prior research on cascading failures within interdependent networks has predominantly emphasized the coupling of nodes. Nevertheless, in practical networks, interactions often exist not just through the nodes themselves but also via the connections (edges) linking them, a configuration referred to as edge-coupled interdependent networks. Past research has shown that introducing a certain percentage of reinforced nodes or connecting edges can prevent catastrophic network collapses. However, the effect of reinforced inter-layer links in edge-coupled interdependent networks has yet to be addressed. Here, we develop a theoretical framework for studying percolation models in edge-coupled interdependent networks by introducing a proportion of reinforced inter-layer links and deriving detailed expressions for the giant and finite components and the percolation phase transition threshold. We find that there exists a required minimum proportion of the reinforced inter-layer links to prevent abrupt network collapse, which serves as a boundary to distinguish different phase transition types of a network. We provide both analytical and numerical solutions for random and scale-free networks, demonstrating that the proposed method exhibits superior reinforcement efficiency compared to intra-layer link reinforcement strategies. Theoretical analysis, simulation results, and real network systems validate our model and indicate that introducing a specific proportion of reinforced inter-layer links can prevent abrupt system failure and enhance network robustness in edge-coupled interdependent networks.

Approximating the Splitting Point of the Swarmalator Model

Swarmalator model attracts the attention of numerous scholars because of its rich dynamical behaviors. We investigate the reason for the phase transition that occurs in a 2D swarmalator model, and conclude that the limit cycle, a reflection of the coexistence of the forces of maintaining and disrupting orders, results in the various clustering phenomena. Through novel mean-field approximation and using the self-consistency argument method, we prove the clustering conditions and the influence of the number of clusters on the existence of clusters, and provide estimates of the cluster size of the splintered phase wave state and the phase transition threshold between the splintered phase wave state and active phase wave state. Due to the widespread presence of nonlinearity, our study is essential to the analysis of clustering phenomena in real physical models.

Quantum-inspired modeling of distributed intelligence systems with artificial intelligent agents self-organization

Distributed intelligence systems (DIS) containing natural and artificial intelligence agents (NIA and AIA) for decision making (DM) belong to promising interdisciplinary studies aimed at digitalization of routine processes in industry, economy, management, and everyday life. In this work, we suggest a novel quantum-inspired approach to investigate the crucial features of DIS consisting of NIAs (users) and AIAs (digital assistants, or avatars). We suppose that N users and their avatars are located in N nodes of a complex avatar - avatar network. The avatars can receive information from and transmit it to each other within this network, while the users obtain information from the outside. The users are associated with their digital assistants and cannot communicate with each other directly. Depending on the meaningfulness/uselessness of the information presented by avatars, users show their attitude making emotional binary “like”/“dislike” responses. To characterize NIA cognitive abilities in a simple DM process, we propose a mapping procedure for the Russell’s valence-arousal circumplex model onto an effective quantum-like two-level system. The DIS aims to maximize the average satisfaction of users via AIAs long-term adaptation to their users. In this regard, we examine the opinion formation and social impact as a result of the collective emotional state evolution occurring in the DIS. We show that generalized cooperativity parameters Gi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i$$\\end{document}, i=1,⋯,N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i=1,\\dots,N$$\\end{document} introduced in this work play a significant role in DIS features reflecting the users activity in possible cooperation and responses to their avatar suggestions. These parameters reveal how frequently AIAs and NIAs communicate with each other accounting the cognitive abilities of NIAs and information losses within the network. We demonstrate that conditions for opinion formation and social impact in the DIS are relevant to the second-order non-equilibrium phase transition. The transition establishes a non-vanishing average information field inherent to information diffusion and long-term avatar adaptation to their users. It occurs above the phase transition threshold, i.e. at Gi>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i>1$$\\end{document}, which implies small (residual) social polarization of the NIAs community. Below the threshold, at weak AIA–NIA coupling (Gi≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i\\le 1$$\\end{document}), many uncertainties in the DIS inhibit opinion formation and social impact for the DM agents due to the information diffusion suppression; the AIAs self-organization within the avatar–avatar network is elucidated in this limit. To increase the users’ impact, we suggest an adaptive approach by establishing a network-dependent coupling rate with their digital assistants. In this case, the mechanism of AIA control helps resolve the DM process in the presence of some uncertainties resulting from the variety of users’ preferences. Our findings open new perspectives in different areas where AIAs become effective teammates for humans to solve common routine problems in network organizations.

Detecting planted partition in sparse multilayer networks

Abstract Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the presence of planted partition among the nodes of a multilayer network with additional nodewise covariate information and diverging average degree, Ma and Nandy (2023, IEEE Trans. Inf. Theory, 69, 3203–3239) introduced Multi-Layer Contextual Stochastic Block Model. In this paper, we consider the problem of detecting planted partitions in the Multi-Layer Contextual Stochastic Block Model, when the average node degrees for each network are greater than $1$. We establish the sharp phase transition threshold for detecting the planted bi-partition. Above the phase-transition threshold testing the presence of a bi-partition is possible, whereas below the threshold no procedure to identify the planted bi-partition can perform better than random guessing. We further establish that the derived detection threshold coincides with the threshold for weak recovery of the partition and provides a quasi-polynomial time algorithm to estimate it.

Percolation transitions in partially edge-coupled interdependent networks with different group size distributions

In many systems, from brain neural networks to epidemic transmission networks, pairwise interactions are insufficient to express complex relationships. Nodes sometimes cooperate and form groups to increase their robustness to risks, and each such group can be considered a “supernode”. Furthermore, previous studies of cascading failures in interdependent networks have typically concentrated on node coupling connections; however, in many realistic scenarios, interactions occur between the edges connecting nodes rather than between the nodes themselves. Networks of this type are called edge-coupled interdependent networks. To better reflect complex networks in the real world, in this paper, we construct a theoretical model of a two-layer partially edge-coupled interdependent network with groups, where all nodes in the same group are functionally dependent on each other. We identify several types of phase transitions, namely, discontinuous, hybrid and continuous, which are determined by the strength of the dependency and the distribution of the supernodes. We first apply our developed mathematical framework to ErdsRnyi and scale-free partially edge-coupled interdependent networks with equally sized groups to analytically and numerically calculate the phase transition thresholds and the critical dependency strengths that distinguish different types of transitions. We then investigate the influence of the group size distribution on cascading failures by presenting examples of two different heterogeneous group size distributions. Our theoretical predictions and numerical findings are in close agreement, demonstrating that decreasing the dependency strength and increasing group size heterogeneity can increase the robustness of interdependent networks. Our results have significant implications for the design and optimization of network security and fill a knowledge gap in the robustness of partially edge-coupled interdependent networks with different group size distributions.

Percolation in interdependent networks with groups and heterogeneous weak interdependency strength under targeted attack

Pairwise dependencies in interdependent networks exist not only between ordinary nodes but also between groups of nodes, where nodes cooperate and form groups to increase their robustness to risks and each group can be considered a ‘supernode’. The interdependencies between supernodes are universal but not always complete and homogeneous. In this paper, we study the robustness of interdependent networks with groups and heterogeneous weak interdependency strength under targeted attack, where the interdependency strength could vary between different supernodes. We identify several types of percolation transitions, namely discontinuous, continuous, and hybrid, which are determined by the structure of the supernodes, the strengths of the interdependencies, and their distributions. We first apply this mathematical framework to the Erdös-Rényi and Scale-free interdependent networks with groups and homogeneous weak interdependency strength to calculate analytically and numerically the values of the phase transition thresholds and the critical interdependency strengths that distinguish different types of transitions. We then present examples of three distributions with different heterogeneous interdependency strengths. Our theoretical and numerical predictions are in close agreement, demonstrating that weaker interdependence strengths and higher levels of interdependence heterogeneity can enhance the robustness of interdependent networks under targeted attack.

In situ visualization of salt crystallization in sub-/supercritical water environments

Elevated temperature and pressure conditions in sub-/supercritical water environments hinder the direct observation of salt crystallization phenomena, resulting in indeterminate salt crystal morphologies. In this study, an innovative experimental apparatus has been developed to conduct in situ investigations into the crystal morphology of various types of inorganic salts. The results indicate that the critical temperature of the water-salt system is higher than that of pure water systems, with phase transition thresholds for saturated NaCl-H2O and KCl-H2O systems 671.4 K and 728.1 K, respectively. A distinct “flash crystallization” phenomenon is observed during the crystallization of inorganic salts, accompanied by different crystal morphologies. KCl crystals exhibit a dispersed particle form, NaCl crystals manifest in a finely fragmented accumulation form, and Na2SO4 crystals present transparent feather-like structures. The size of NaCl crystals formed on the surface of a Ni wire at 622.8 K through heterogeneous nucleation ranges from 200.4 μm to 450.9 μm. The crystallization characteristics of salt in sub-/supercritical water are influenced by various factors, including electric dipole moment interactions, common ion effect, the effect of type I salts on type II salts, and homo/heterogeneous nucleation.

VO2 Films Decorated with an MXene Interface for Decreased-Power-Triggered Terahertz Modulation.

VO2, which exhibits semiconductor-metal phase transition characteristics occurring on a picosecond time scale, holds great promise for ultrafast terahertz modulation in next-generation communication. However, as of now, there is no reported prototype for an ultrafast device. The temperature effect has been proposed as one of the major obstacles. Consequently, reducing the excitation threshold for the phase transition would be highly significant. The traditional strategy typically involves chemical doping, but this approach often leads to a decrease in phase transition amplitude and a slower transition speed. In this work, we proposed a design featuring a highly conductive MXene interfacial layer between the VO2 film and the substrate. We demonstrate a significant reduction in the phase transition threshold for both temperature and laser-induced phase transition by adjusting the conductivity of the MXene layers with varying thicknesses. Our observations show that the phase transition temperature can be decreased by 9 °C, while the pump fluence for laser excitation can be reduced by as high as 36%. The ultrafast phase transition process on a picosecond scale, as revealed by the optical-pump terahertz-probe method, suggests that the MXene layers have minimal impact on the phase transition speed. Moreover, the reduced phase transition threshold can remarkably alleviate the photothermal effect and inhibit temperature rise and diffusion in VO2 triggered by laser. This study offers a blueprint for designing VO2/MXene hybrid films with reduced phase transition thresholds. It holds significant potential for the development of low-power, intelligent optical and electrical devices including, but not limited to, terahertz modulators based on phase transition phenomena.

Entropy-Driven Phase Transition in Nanonucleation via Reciprocal Relations.

Depletion forces, commonly modeled with rigid body assumptions, inadequately describe nanoparticle behavior. This study introduces the roles of Soret and Dufour effects in nanoparticle systems, focusing on mass and energy gradient interchange. The Dufour effect drives energy flow through mass gradients, which implies the possibility of driving the energy flow near the nanoparticles to induce phase transitions via manipulating the monomer concentrations. Our experimental platform confirmed these theories, synthesizing HCP quantum dots from Au, Ag, Pd, and mixed halide perovskites under varied precursor concentrations. By analyzing energy flow and nucleation dynamics through the Dufour effect, we mapped phase transition thresholds, linking them to material entropy. This study provides insight into nanoparticle assembly and phase behavior, highlighting the significance of entropy in nucleation dynamics.

Continuous modulation of VO2 film’s phase transition threshold and transmittance via n-AZO/n-VO2 heterojunction

To solve the irreconcilable contradiction between the phase transition threshold and the optical property of VO2 film, an n-AZO/n-VO2 heterojunction, in which AZO is Al-doped ZnO, was constructed with the radio frequency (RF) magnetron sputtering and the post annealing. The effects of annealing on the composition and properties of vanadium oxide films have been investigated, as well as the effects of annealing and AZO layer thickness on the phase transition performance of the n-AZO/n-VO2 heterojunction. The results indicate that the V2O5 film will gradually transform into VO2 (M) through V6O13 and VO2 (B) during the reduction annealing at 500 °C. The phase transition temperature (Tc) of VO2 (M) film increases with the annealing temperature. In the heterojunction formed by the ohmic contact between AZO and VO2 layers, the free electrons will be injected into the VO2 layer from AZO layer, which reduces the heterojunction’s Tc from 69.2 to 41.5 °C. The first-principles calculations were performed with the Vienna Ab initio Simulation Package (VASP) to assist in the influence mechanism explanation. In addition to modulating Tc, the AZO layer in the heterojunction also plays an antireflection role, increasing the maximum visible transmittance of VO2 film by ∼ 10 %.

Influence of iron anisotropy on phase transition near grain boundary under shock

As is well known, iron plays an important role in the fields of national defense and industry, so it is of great significance to study its behavior under dynamic high pressure. As one of the most common defects in metals in nature, grain boundaries have an important influence on the mechanical properties and deformation of materials under shock. This work intends to use large-scale non-equilibrium molecular dynamics simulation to study the influence of iron anisotropy on the phase transition in bicrystal under shock loading. By tracking the local structure, shear stress distribution and morphology characteristics after shock on both sides of the grain boundaries, the factors affecting the response on both sides of the grain boundary are analyzed. Our research result shows that shocking along the non-centrosymmetric grain direction can cause significant differences in the phase transition threshold, path and mode on both sides of the symmetric grain boundary. Especially, the different phase transition dynamic processes on both sides of the sigma11 grain boundary are discussed in detail in this work, which have been rarely discussed in previous studies. Considering the symmetry of the microstructure on both sides of this type of grain boundary, the result of asymmetric shock response is different from people’s inertial cognition. Finally, it is found that the atoms in both models will shift along the direction perpendicular to the shocked direction under shock, indicating that the shock wave generated by the piston method should no longer be simply regarded as one-dimensional when shocked along the non centrosymmetric crystal direction, and the displacement of atoms along the direction perpendicular to the shocked direction is closely related to the symmetry of the crystal, which causes significant differences in shear stress on both sides of the grain boundary and ultimately affects the shock response. This study reveals that the anisotropy of lattice has an important effect on the phase transition on both sides of grain boundaries under shock loading, which can provide theoretical support for the experimental studies of polycrystalline metals and alloys under shock.

Enhanced Nitrate Fraction: Enabling Urban Aerosol Particles to Remain in a Liquid State at Reduced Relative Humidity

AbstractNitrate has become the primary inorganic compound in urban aerosol particles, but its effects on particle phase state, which is crucial in multiphase chemistry, remains largely unknown. Herein, particle rebound measurements were conducted to explore the relationship between the liquid–phase–transition threshold relative humidity (RHthreshold) and the inorganic compounds mass fraction in dry particles (Finorg). Results revealed negative correlations between RHthreshold and Finorg, with more nitrate leading to lower RHthreshold. Even with RH < 20%, particles with ∼50% nitrate mass fraction remained in non‐solid state. Taking Beijing as an example, decreases were observed in RHthreshold from 64% in 2015 to below 53% nowadays during the moderate‐pollution periods (PM2.5 = 35–75 μg/m3) due to an enhanced nitrate fraction. This allowed urban aerosol particles to exist in liquid state at lower RH, and consequently, kinetic limitation by bulk diffusion in nitrate‐dominated particles might be negligible, making them key seeds for secondary aerosol formation through multiphase reactions.

Percolation phase transition in the heterogeneous multi-coupled interdependent network

In previous studies, complex system models have often been set up in an oversimplified manner and the failure mechanism for nodes affected by each other is not correspond to reality. Accordingly, we develop a new model of heterogeneous multi-coupled interdependent networks and analyze the change in the giant component of the network after the attack in conjunction with the load redistribution mechanism. We first analyze the cascading failure process of the network analytically by recursive methods, estimate the critical phase transition threshold and the size of the giant component of the remaining network after network percolation, and find that the threshold of the WS sub-network is positively related to the average degree, and the BA sub-network is related to the power exponent λ of the distribution. When λ is less than or equal to 2, there is always a giant component in the network. After λ is greater than 3.4788⋯, there is no giant component. When λ is between 2 to 3.4788⋯, we found that the threshold of the sub-network is more influenced by the proportion of attacks (p1 and p2), and when p1 is larger, the sub-networks interact with each other, resulting in a smaller threshold for the BA sub-network, while the threshold of the WS sub-network is smaller in other cases. Finally, the cross-sectional comparison illustrates that as λ increases to 3.4788⋯, the robustness of the BA sub-network increases, contrary to the findings for single-layer networks. Overall, the heterogeneous multi-coupled interdependent network is more robust, and the giant component is greatly affected by the low robust sub-network, but its existence is related to the stock of nodes.

Phase Transition Threshold and Stability of Magnetic Skyrmions

Phase Transition Threshold and Stability of Magnetic Skyrmions

A chemotactic microrobot with integrated iridescent surface for optical-tracking

Recent advancements in materials, nanofabrication, actuation, and sensing have facilitated the development of untethered microrobots. However, realizing sub-millimeter-integrated microrobots with actuation, perception, and wireless communication capabilities remains elusive. In this study, we present the successful fabrication of chemotactic microrobots at the micron scale, featuring integrated iridescent structural color surfaces that can be utilized for robot motion control through optical tracking. Using a pH-responsive biopolymer as the carrier, we have created microrobots that employ bilayer joints, mimicking the actuation characteristics observed in arthropods. Additionally, biomimetic microstructures with structural color functionality have been incorporated onto the surface of the robots, serving as an optical-communication skin. The robots are actuated through reversible expansion triggered at the phase transition threshold of the biopolymer, while their geometric states and posture information are acquired by converting the volume strain into color variations. This research can potentially establish a critical pathway for developing state-feedback-controlled microrobots for future biomedical applications.

Impact of the uniaxial strain on terahertz modulation characteristics in flexible epitaxial VO2 film across the phase transition.

Exploring flexible electronics is on the verge of innovative breakthroughs in terahertz (THz) communication technology. Vanadium dioxide (VO2) with insulator-metal transition (IMT) has excellent application potential in various THz smart devices, but the associated THz modulation properties in the flexible state have rarely been reported. Herein, we deposited an epitaxial VO2 film on a flexible mica substrate via pulsed-laser deposition and investigated its THz modulation properties under different uniaxial strains across the phase transition. It was observed that the THz modulation depth increases under compressive strain and decreases under tensile strain. Moreover, the phase-transition threshold depends on the uniaxial strain. Particularly, the rate of the phase transition temperature depends on the uniaxial strain and reaches approximately 6 °C/% in the temperature-induced phase transition. The optical trigger threshold in laser-induced phase transition decreased by 38.9% under compressive strain but increased by 36.7% under tensile strain, compared to the initial state without uniaxial strain. These findings demonstrate the uniaxial strain-induced low-power triggered THz modulation and provide new insights for applying phase transition oxide films in THz flexible electronics.

The maximum solubility product marks the threshold for condensation of multivalent biomolecules

Clustering of weakly interacting multivalent biomolecules underlies the formation of membraneless compartments known as condensates. As opposed to single-component (homotypic) systems, the concentration dependence of multicomponent (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multicomponent systems. In this study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intracluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the SP profiles. The interplay of flexibility, length, and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when SPs are normalized to nondimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering versus concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates.

Smart "Thrombus": Self-Localizing UCST-Type Microcage.

Embolization is often used to block blood supply for controlling the growth of fibroids and malignant tumors, but limited by embolic agents lacking spontaneous targeting and post-treatment removal. So we first adopted nonionic poly(acrylamide-co-acrylonitrile) with an upper critical solution temperature (UCST) to build up self-localizing microcages by inverse emulsification. The results showed that these UCST-type microcages behaved with the appropriate phase-transition threshold value around 40 °C, and spontaneously underwent an expansion-fusion-fission cycle under the stimulus of mild temperature hyperthermia. Given the simultaneous local release of cargoes, this simple but smart microcage is expected to act as a multifunctional embolic agent for tumorous starving therapy, tumor chemotherapy, and imaging.

The concentration threshold for condensation of multivalent molecules is set by by the maximum solubility product.

Clustering of weakly interacting multivalent biomolecules underlies the formation of membrane-less compartments known as condensates. As opposed to single component (homotypic) systems, the concentration dependence of multi-component (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multi-component systems. In the current study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intra-cluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the solubility product profiles. The interplay of flexibility, length and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when solubility products are normalized to non-dimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering vs. concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates. (Supported by NIGMS grants R24 GM137787 and R01 GM132859.)