Abrupt Phase Transition Research Articles

Optomechanical interaction between single-walled carbon nanotubes of various structures

We consider optomechanical interaction in an asymmetric structure of a carbon nanotubes dimer of different orientations and/or different atomic structures in the field of a plane wave or a focused Gaussian beam. Here we show that optical coupling in such the system can lead to nonreciprocal interactions between the constituents. We demonstrate that a non-conservative force is applied to the center of mass of an optically coupled nanotube dimer, resulting in an unexpected lateral action. The sign and magnitude of this force depend on abrupt phase transitions in the properties of the asymmetric dimer.

Concurrent Structural and Electronic Phase Transitions in V2O3 Thin Films with Sharp Resistivity ChangeSupported by the National Key R&D Program of China (Grant No. 2017YFA0403600), and Joint Funds of the National Natural Science Foundation of China and the Chinese Academy of Sciences Large-Scale Scientific Facility (Grant No. U1532149).

The relationship between structural and electronic phase transitions in V2O3 thin films is of critical importance for understanding of the mechanism behind metal–insulator transition (MIT) and related technological applications. Despite being extensively studied, there are currently no clear consensus and picture of the relation between structural and electronic phase transitions so far. Using V2O3 thin films grown on r-plane Al2O3 substrates, which exhibit abrupt MIT and structural phase transition, we show that the electronic phase transition occurs concurrently with the structural phase transition as revealed by the electrical transport and Raman spectra measurements. Our result provides experimental evidence for clarifying this issue, which could form the basis of theoretical studies as well as technological applications in V2O3.

Absolute calibration of the latent heat of transition using differential thermal analysis.

We describe a simple and accurate differential thermal analysis setup to measure the latent heat of solid state materials undergoing abrupt phase transitions in the temperature range from 77K to above room temperature. We report a numerical technique for the absolute calibration of the latent heat of transition without the need for a reference sample. The technique is applied to three different samples-vanadium sesquioxide undergoing the Mott transition, bismuth barium ruthenate undergoing a magnetoelastic transition, and an intermetallic Heusler compound. In each case, the inferred latent heat value agrees with the literature value within its error margins. To further demonstrate the importance of absolute calibration, we show that the changes in the latent heat of the Mott transition in vanadium sesquioxide (V2O3) remain constant to within 2% even as the depth of supersaturation changes by about 10K in non-equilibrium dynamic hysteresis measurements. We also apply this technique for the measurement of the temperature-dependent specific heat.

Incommensurate smectic phase in close proximity to the high-Tc superconductor FeSe/SrTiO3

Superconductivity is significantly enhanced in monolayer FeSe grown on SrTiO3, but not for multilayer films, in which large strength of nematicity develops. However, the link between the high-transition temperature superconductivity in monolayer and the correlation related nematicity in multilayer FeSe films is not well understood. Here, we use low-temperature scanning tunneling microscopy to study few-layer FeSe thin films grown by molecular beam epitaxy. We observe an incommensurate long-range smectic phase, which solely appears in bilayer FeSe films. The smectic order still locally exists and gradually fades away with increasing film thickness, while it suddenly vanishes in monolayer FeSe, indicative of an abrupt smectic phase transition. Surface alkali-metal doping can suppress the smectic phase and induce high-Tc superconductivity in bilayer FeSe. Our observations provide evidence that the monolayer FeSe is in close proximity to the smectic phase, and its superconductivity is likely enhanced by this electronic instability as well.

Multiple abrupt phase transitions in urban transport congestion

During the last decades, the study of cities has been transformed by new approaches combining engineering and complexity sciences. Network theory is playing a central role, facilitating the quantitative analysis of crucial urban dynamics, such as mobility, city growth or urban planning. In this work, we focus on the spatial aspects of congestion. Analyzing a large amount of real city networks, we show that the location of the onset of congestion changes according to the considered urban area, defining, in turn, a set of congestion regimes separated by abrupt transitions. To help unveiling these spatial dependencies of congestion (in terms of network betweenness analysis), we introduce a family of planar road network models composed of a dense urban center connected to an arboreal periphery. These models, coined as GT and DT-MST models, allow us to analytically, numerically and experimentally describe how and why congestion emerges in particular geographical areas of monocentric cities and, subsequently, to describe the congestion regimes and the factors that promote the appearance of their abrupt transitions. We show that the fundamental ingredient behind the observed abrupt transitions is the spatial separation between the urban center and the periphery, and the number of separate areas that form the periphery. Elaborating on the implications of our results, we show that they may have an influence on the design and optimization of road networks regarding urban growth and the management of daily traffic dynamics.

Photochemical-induced phase transitions in photoactive semicrystalline polymers.

The emergent photoactive materials obtained through photochemistry make it possible to directly convert photon energy to mechanical work. There has been much recent work in developing appropriate materials, and a promising system is semicrystalline polymers of the photoactive molecule azobenzene. We develop a phase field model with two order parameters for the crystal-melt transition and the trans-cis photoisomerization to understand such materials, and the model describes the rich phenomenology. We find that the photoreaction rate depends sensitively on temperature: At temperatures below the crystal-melt transition temperature, photoreaction is collective, requires a critical light intensity, and shows an abrupt first-order phase transition manifesting nucleation and growth; at temperatures above the transition temperature, photoreaction is independent and follows first-order kinetics. Further, the phase transition depends significantly on the exact forms of spontaneous strain during the crystal-melt and trans-cis transitions. A nonmonotonic change of photopersistent cis ratio with increasing temperature is observed accompanied by a reentrant crystallization of trans below the melting temperature. A pseudo phase diagram is subsequently presented with varying temperature and light intensity along with the resulting actuation strain. These insights can assist the further development of these materials.

Topological phase transition in the periodically forced Kuramoto model

A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18 , 043128 (2008)], identifying all bifurcations within the model. We show that the phase diagram predicted by this analysis is incomplete. Our numerical analysis of the equations reveals that the model can also undergo an abrupt phase transition from oscillations to wobbly rotations of the order parameter under increasing field frequency or decreasing field strength. This transition was not revealed by bifurcation analysis because it is not caused by a bifurcation, and can neither be classified as first nor second-order since it does not display critical phenomena characteristic of either transition. We discuss the topological origin of this transition and show that it is determined by a singular point in the order-parameter space.

Percolation on coupled networks with multiple effective dependency links.

The ubiquitous coupled relationship between network systems has become an essential paradigm to depict complex systems. A remarkable property in the coupled complex systems is that a functional node should have multiple external support associations in addition to maintaining the connectivity of the local network. In this paper, we develop a theoretical framework to study the structural robustness of the coupled network with multiple useful dependency links. It is defined that a functional node has the broadest connectivity within the internal network and requires at least M support link of the other network to function. In this model, we present exact analytical expressions for the process of cascading failures, the fraction of functional nodes in the stable state, and provide a calculation method of the critical threshold. The results indicate that the system undergoes an abrupt phase transition behavior after initial failure. Moreover, the minimum inner and inter-connectivity density to maintain system survival is graphically presented at different multiple effective dependency links. Furthermore, we find that the system needs more internal connection densities to avoid collapse when it requires more effective support links. These findings allow us to reveal the details of a more realistic coupled complex system and develop efficient approaches for designing resilient infrastructure.

Abrupt phase transition of epidemic spreading in simplicial complexes

Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading, using the Susceptible-Infected-Susceptible (SIS) model, in simplicial complexes. In particular, we analyze the dynamics of SIS in complex networks characterized by pairwise interactions (links), and three-body interactions (filled triangles, also known as 2-simplices). This higher-order description of the epidemic spreading is analytically formulated using a microscopic Markov chain approximation. The analysis of the fixed point solutions of the model, reveal an interesting phase transition that becomes abrupt with the infectivity parameter of the 2-simplices. Our results pave the way for network theorists to advance in our physical understanding of epidemic spreading in real scenarios where diseases are transmitted among groups as well as among pairs, and to better understand the behaviour of dynamical processes in simplicial complexes.

Weyl symmetry in stochastic quantum gravity

We propose that the gauge principle of d-dimensional Euclidean quantum gravity is Weyl invariance in its stochastic -dimensional bulk. Observables are defined as depending only on conformal classes of d-dimensional metrics. We work with the second order stochastic quantization of Einstein equations in a -dimensional bulk. There, the evolution is governed by the stochastic time, which foliates the bulk into Euclidean d-dimensional leaves. The internal metric of each leaf can be parametrized by its unimodular part and conformal factor. Additional bulk metric components are the ADM stochastic lapse and a stochastic shift. The Langevin equation determines the acceleration of the leaf as the sum of a quantum noise, a drift force proportional to Einstein equations and a viscous first order force. Using Weyl covariant decomposition, this Langevin equation splits into irreducible stochastic equations, one for the unimodular part of the metric and one for its conformal factor. For the first order Langevin equation, the unphysical fields are the conformal factor, which is a classical spectator, and the stochastic lapse and shift. These fields can be gauge-fixed in a BRST invariant way in function of the initial data of the process. One gets observables that are covariant with respect to internal reparametrization in each leaf, and invariant under arbitrary reparametrization of the stochastic time. The interpretation of physical observable at finite stochastic time is encoded in a transitory -dimensional phase where the Lorentz time cannot be defined. The latter emerges in the infinite stochastic time limit by an abrupt phase transition from quantum to classical gravity.

Percolation analysis of urban air quality: A case in China

Air pollution has caused widespread environmental and public health problems and aroused significant attention around the world. Based on the daily air quality index (AQI) data of 35 major cities in China, the cross-correlation functions of time lags between cities are calculated and a sequence of time-evolving directed and weighted AQI correlation networks is built. The probability distribution of correlations is separated into positive and negative parts. The probability distribution of time lag exhibits that the effect of time lag is clear for cities with negative correlations and not for cities with positive correlations. Further, percolation theory technique is put forward to analyze the behavior of connected clusters in the correlation networks. The results show that abrupt phase transition usually occurs between three to six weeks ahead of the peak or valley point of the evolution of AQIs mean for highly polluted region, which suggests that this event can make an alarm. The method and results presented not only improve the understanding of the climate effects and correlated effects of AQIs, but also facilitate the study of air pollution forecasting and warning.

Nontrivial resource requirement in the early stage for containment of epidemics

During epidemic control, containment of the disease is usually achieved through increasing a devoted resource to reduce the infectiousness. However, the impact of this resource expenditure has not been studied quantitatively. For disease spread, the recovery rate can be positively correlated with the average amount of resource devoted to infected individuals. By incorporating this relation we build a novel model and find that insufficient resource leads to an abrupt increase in the infected population size, which is in marked contrast with the continuous phase transitions believed previously. Counterintuitively, this abrupt phase transition is more pronounced in less contagious diseases. Furthermore, we find that even for a single infection source, the public resource needs to be available in a significant amount, which is proportional to the total population size, to ensure epidemic containment. Our findings provide a theoretical foundation for efficient epidemic containment strategies in the early stage.

Percolation Phase Transition from Ionic Liquids to Ionic Liquid Crystals

Due to their complex molecular structures and interactions, phase behaviors of complex fluids are quite often difficult to be identified by common phase transition analysis methods. Percolation phase transition, on the other hand, only monitors the degree of connection among particles without strict geometric requirements such as translational or orientational order, and thus suitable for pinpointing phase transitions of complex fluids. As typical complex fluids, ionic liquids (ILs) exhibit phases beyond the description of simple liquid theories. In particular, with an intermediate cationic side-chain length, ILs can form the nanoscale segregated liquid (NSL) state, which will eventually transform into the ionic liquid crystal (ILC) structure when the side chains are adequately long. However, the microscopic mechanism of this transformation is still unclear. In this work, by means of coarse-grained molecular dynamics simulation, we show that, with increasing cationic side-chain length, some local pieces of non-polar domains are gradually formed by side chains aligned in parallel inside the NSL phase, before an abrupt percolation phase transition happens when the system transforms into the ILC phase. This work not only identifies that the NSL to ILC phase transition is a critical phenomenon, but also demonstrates the importance of percolation theory to complex fluids.

Phase transitions in normalized cut of social networks

One of the main goals of network analysis and data science is to identify community structures in a network. Community structure is a typical feature of social networks and community detection is considered to be crucial to understand the structure and function of social networks in cyberspace. The community detection problem of social networks can be viewed as a graph partitioning problem whose objective is to identify the external edges as the edge cut that separates the network as two subnetworks by recursive method. The degree-normalized adjacency matrix is more convenient than traditional Laplacian matrix in calculating eigenvalues and eigenvectors. In this work, based on random model we first prove the existence of an abrupt phase transition for community detection in terms of the degree-normalized adjacency matrix with accurate critical value. In detail, the detectability of community detection has changed from high to low when the critical value of phase transition q approaches p1p2 almost surely, where pi(i=1,2) is the intra-community edge connection probability of subnetworks Ci, respectively. Then, the validity of the theoretical results is verified by numerical experiments.

Fragility and anomalous susceptibility of weakly interacting networks.

Percolation is a fundamental concept that has brought new understanding of the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much fewer interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transitions are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer and has a well-defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers and is characterized by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous behavior of the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon, using a susceptibility measure that defines the range where the abrupt transition is more likely to occur. Finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition.

Critical transitions in heterogeneous networks: Loss of low-degree nodes as an early warning signal.

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

Physiological tipping points to light reduction underlie seagrass population collapse and abrupt shift in a shallow coastal lagoon

Physiological tipping points to light reduction underlie seagrass population collapse and abrupt shift in a shallow coastal lagoon

Feedback-induced critical behavior in binary propagation on complex networks

While the phase transitions in binary propagation on complex networks have been studied a great deal from diverse fields during the past years, the effect of feedback has rarely been systematically addressed in a general manner. Here, we study a minimal network model of binary propagation with a general feedback effect. It is found that when the basic propagation rate is small, moderate positive feedback can induce bistable dynamics, resulting in an abrupt and discontinuous phase transition, which is absent in the case of negative feedback or no feedback. Moreover, the degree heterogeneity of the network further induces a hysteresis loop structure in this phase transition. It is also found that positive feedback accelerates spread before reaching the peak activity, whereas negative feedback has a contrary effect, which may uncover the origin of the accelerating spread observed in sophisticated models [S. V. Scarpino, A. Allard, and L. H\'ebert-Dufresne, Nat. Phys. 12, 1042 (2016)]. These findings reveal the universal and nontrivial effects of feedback on binary propagation dynamics. It can help to preestimate the phase-transition behavior in specific network propagation models and help to better understand the criticality of other dynamical processes on complex networks arising from different scientific backgrounds.

Evaluation of ENSO simulations in CMIP5 models: A new perspective based on percolation phase transition in complex networks

In this study, the performance of CMIP5 models in simulating the El Niño-Southern Oscillation (ENSO) is evaluated by using a new metric based on percolation theory. The surface air temperatures (SATs) over the tropical Pacific Ocean are constructed as a SAT network, and the nodes within the network are linked if they are highly connected (e.g., high correlations). It has been confirmed from reanalysis datasets that the SAT network undergoes an abrupt percolation phase transition when the influences of the sea surface temperature anomalies (SSTAs) below are strong enough. However, from simulations of the CMIP5 models, most models are found incapable of capturing the observed phase transition at a proper critical point Pc. For the 15 considered models, four even miss the phase transition, indicating that the simulated SAT network is too stable to be significantly changed by the SSTA below. Only four models can be considered cautiously with some skills in simulating the observed phase transition of the SAT network. By comparing the simulated SSTA patterns with the node vulnerabilities, which is the chance of each node being isolated during a ENSO event, we find that the improperly simulated sea-air interactions are responsible for the missing of the observed percolation phase transition. Accordingly, a careful study of the sea-air couplers, as well as the atmospheric components of the CMIP5 models is suggested. Since the percolation phase transition of the SAT network is a useful phenomenon to indicate whether the ENSO impacts can be transferred remotely, it deserves more attention for future model development.

Packet transmission with a lifetime constraint in scale-free networks

In this paper, we study how the lifetime of packets impacts the overall transmission capacity of scale-free communication networks. In our model, we observed an abrupt phase transition of packet loss rate when the packet generation rate increases, based on which we redefined the network capacity as the critical packet generation rate of packet loss. Then, we found a sharp phase transition of network capacity with the increase of packet lifetime, which is also predicted by our analytical results of network capacity. Moreover, we obtained that there is an optimal routing parameter of the tunable path routing algorithm corresponding to the maximum network capacity. Finally, we discussed the influence of network topological structure on the network capacity.