Abrupt Phase Transition Research Articles

TwofoldPTsymmetry in doubly exponential optical lattices

We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of $\mathcal{PT}$ symmetry is not around zero and the potential satisfies a shifted $\mathcal{PT}\text{-symmetry}$ relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted $\mathcal{PT}\text{-symmetric}$ relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.

Exploring the influence of the poly(4-vinyl pyridine) segment on the solution properties and thermal phase behaviours of oligo(ethylene glycol) methacrylate-based block copolymers: the different aggregation processes with various morphologies.

The assembly properties, thermal phase behavior and microdynamics of well-defined P(MEO2MA-co-OEGMA)-b-P4VP, (poly(2-(2-methoxyethoxy)ethylmethacrylate)-co-poly(oligo(ethylene glycol) methacrylate))-b-poly(4-vinyl pyridine), in aqueous solution during heating are investigated in detail by dynamic light scattering (DLS), turbidity measurements, temperature-variable (1)H NMR and FTIR spectroscopy in combination with two-dimensional correlation spectroscopy (2Dcos) and the perturbation correlation moving window (PCMW) technique. It is observed that the chain length of the relatively hydrophobic P4VP segment strongly affects the temperature-induced phase transition behavior of the block copolymers: the copolymers with shorter P4VP7/10 segments exhibit an abrupt phase transition process, while the copolymer with longer P4VP19 blocks presents a relatively gradual transition behavior. Moreover, the two systems with different P4VP segment lengths have different morphologies in aqueous solution: a single-chain globule for shorter P4VP7/10 systems and a core-shell micelle consisting of a relatively hydrophobic P4VP core and a hydrophilic POEGMA-based shell for the longer P4VP19 system. Analysis of spectral results clearly illustrates that the dehydration of the C[double bond, length as m-dash]O groups at the linkages between backbones and pendant chains predominates the sharp phase transition of P(MEO2MA-co-OEGMA)-b-P4VP10, while the dehydration of hydrophobic C-H groups on the side chains in P(MEO2MA-co-OEGMA)-b-P4VP19 leads to the continuous increase of the hydrodynamic diameter (Dh) upon heating.

Phase-Changing Bistable Electroactive Polymer Exhibiting Sharp Rigid-to-Rubbery Transition

A phase-changing polymer comprising stearyl acrylate and a long-chain urethane diacrylate was studied as a new bistable electroactive polymer. The abrupt and reversible phase transition of the crystalline aggregates of the stearyl moieties results in a rapid shift between the rigid and rubbery states of the polymers during temperature cycles. The transition temperature is tunable between 34–46 °C. A storage modulus change of ∼1000 fold can be obtained within a narrow temperature range of 10 °C. The polymer shows excellent shape memory properties with both fixation rate and recovery rate close to 100%. Diaphragm actuators based on the polymer thin films were electrically actuated up to 70% strain at 50 °C. The actuated shape can be “frozen” after the films were allowed to cool below the transition temperature. This rigid-to-rigid deformation is refreshable and repeatable via the rigid-to-rubbery transition and electrical actuation in the rubbery state.

In Situ TEM Nanoindentation Studies on Stress-Induced Phase Transformations in Metallic Materials

Although abundant phase transformations are in general thermally driven processes, there are many examples wherein stresses can induce phase transformations. Numerous in situ techniques, such as in situ x-ray diffraction and neutron diffraction, have been applied to reveal phase transformations. Recently, an in situ nanoindentation technique coupled with transmission electron microscopy demonstrated the capability to directly correlating stresses with phase transformations and microstructural evolutions at a submicron length scale. Here we briefly review in situ studies on stress-induced diffusional and diffusionless phase transformations in amorphous CuZrAl alloy and NiFeGa shape memory alloy. In the amorphous CuZrAl, in situ nanoindentation studies show that the nucleation of nanocrystals (a diffusional process) occurs at ultra-low stresses manifested by a prominent stress drop. In the NiFeGa shape memory alloy, two distinctive types of martensitic (diffusionless) phase transformations accompanied by stress plateaus are observed, including a reversible gradual phase transformation at low stress levels, and an irreversible abrupt phase transition at higher stress levels.

A Bayesian Interpretation of First-Order Phase Transitions

The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat and entropy difference between phases will inevitably have an equivalent in any problem of inferring the result of a yes/no question, given information in the form of expectation values.

Parity-time-symmetric coupled microring lasers operating around an exceptional point.

The behavior of a parity-time-symmetric coupled microring system is studied when operating in the vicinity of an exceptional point. Using the abrupt phase transition around this point, stable single-mode lasing is demonstrated in spectrally multimoded microring arrangements.

Magnetic phase diagram of graphene nanorings in an electric field

Magnetic properties of graphene nanorings are investigated in the presence of an electric field. Within the formalism of Hubbard model, the graphene nanorings of various geometric configurations are found to exhibit rich phase diagram. For a nanoring system which has degenerate states at the Fermi level, the system is shown to undergo an abrupt phase transition from the antiferromagnetic to a nonmagnetic state in an electric field applied cross its zigzag edges. However, the nanoring is found to always stay in the antiferromagnetic state when the electric field is applied cross its armchair edges. For the other nanoring system with a finite single-particle gap, the magnetic moments of its antiferromagnetic ground state is seen to decrease gradually to zero with the electric field applied cross the zigzag edges. When the electric field is applied cross the armchair edges, the nanoring is shown to undergo several magnetic phase transitions before settling itself in a nonmagnetic ordering.

Sub-Kelvin magnetic and electrical measurements in a diamond anvil cell with in situ tunability.

We discuss techniques for performing continuous measurements across a wide range of pressure-field-temperature phase space, combining the milli-Kelvin temperatures of a helium dilution refrigerator with the giga-Pascal pressures of a diamond anvil cell and the Tesla magnetic fields of a superconducting magnet. With a view towards minimizing remnant magnetic fields and background magnetic susceptibility, we characterize high-strength superalloy materials for the pressure cell assembly, which allows high fidelity measurements of low-field phenomena such as superconductivity below 100 mK at pressures above 10 GPa. In situ tunability and measurement of the pressure permit experiments over a wide range of pressure, while at the same time making possible precise steps across abrupt phase transitions such as those from insulator to metal.

A steep-slope transistor based on abrupt electronic phase transition.

Collective interactions in functional materials can enable novel macroscopic properties like insulator-to-metal transitions. While implementing such materials into field-effect-transistor technology can potentially augment current state-of-the-art devices by providing unique routes to overcome their conventional limits, attempts to harness the insulator-to-metal transition for high-performance transistors have experienced little success. Here, we demonstrate a pathway for harnessing the abrupt resistivity transformation across the insulator-to-metal transition in vanadium dioxide (VO2), to design a hybrid-phase-transition field-effect transistor that exhibits gate controlled steep (‘sub-kT/q') and reversible switching at room temperature. The transistor design, wherein VO2 is implemented in series with the field-effect transistor's source rather than into the channel, exploits negative differential resistance induced across the VO2 to create an internal amplifier that facilitates enhanced performance over a conventional field-effect transistor. Our approach enables low-voltage complementary n-type and p-type transistor operation as demonstrated here, and is applicable to other insulator-to-metal transition materials, offering tantalizing possibilities for energy-efficient logic and memory applications.

Phase Transitions in Spectral Community Detection

Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external edges as the graph cut that separates these two subnetworks. In this paper, we consider a general model where two arbitrarily connected subnetworks are connected by random external edges. Using random matrix theory and concentration inequalities, we show that when one performs community detection via spectral clustering there exists an abrupt phase transition as a function of the random external edge connection probability. Specifically, the community detection performance transitions from almost perfect detectability to low detectability near some critical value of the random external edge connection probability. We derive upper and lower bounds on the critical value and show that the bounds are equal to each other when two subnetwork sizes are identical. Using simulated and experimental data we show how these bounds can be empirically estimated to validate the detection reliability of any discovered communities.

Actio et reactio in optical binding.

The symmetry in action and reaction between interacting particulate matter breaks down when the interaction is mediated by an out-of-equilibrium environment. Nevertheless, even in this case, the space translational invariance still imposes the conservation of canonical momentum. Here we show that optical binding of an asymmetric material system can result in non-reciprocal interactions between constituents. We demonstrate that a non-conservative force applies to the center of mass of an optically bound dimer of dissimilar particles, which leads to an unexpected action in the transversal direction. The sign and the magnitude of this positional force depend on the abrupt phase transitions in the properties of the asymmetric dimer.

Clusters—The Seeds of Droplets and Snowflakes

The clusters play a significant role in formation of Universe, in the condensation of matter and meteorological phenomena, in processes of life, and in our technologies. Therefore, they should be studied better. Modern electronic thermophysical databases are very rich sources of knowledge about cluster properties. This research is directed towards development and perfection of methods to extract properties of clusters from precise thermophysical data. The parallel between clusters, droplets and snowflakes helps in this investigation. The paper shows the achievements and discoveries on this way. The soft structural transition in cluster fractions is opposed to the abrupt phase transition at a condensation of matter.

Rounding of abrupt phase transitions in brain networks

The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as its robustness, is a major challenge in contemporary neuroscience. Here, we present an extensive numerical study of a family of simple dynamical models, which describe activity propagation in brain networks through the integration of different neighboring spiking potentials, mimicking basic neural interactions. The requirement of signal integration may lead to discontinuous phase transitions in networks that are well described by the mean-field approximation, thus preventing the emergence of critical points in such systems. Brain networks, however, are finite dimensional and exhibit a heterogeneous hierarchical structure that cannot be encoded in mean-field models. Here we propose that, as a consequence of the presence of such a heterogeneous substrate with its concomitant structural disorder, critical-like features may emerge even in the presence of integration. These conclusions may prove significant in explaining the observation of traits of critical behavior in large-scale measurements of brain activity.

Exact solution for first-order synchronization transition in a generalized Kuramoto model.

First-order, or discontinuous, synchronization transition, i.e. an abrupt and irreversible phase transition with hysteresis to the synchronized state of coupled oscillators, has attracted much attention along the past years. We here report the analytical solution of a generalized Kuramoto model, and derive a series of exact results for the first-order synchronization transition, including i) the exact, generic, solutions for the critical coupling strengths for both the forward and backward transitions, ii) the closed form of the forward transition point and the linear stability analysis for the incoherent state (for a Lorentzian frequency distribution), and iii) the closed forms for both the stable and unstable coherent states (and their stabilities) for the backward transition. Our results, together with elucidating the first-order nature of the transition, provide insights on the mechanisms at the basis of such a synchronization phenomenon.

Continuous tuning of W-doped VO2 optical properties for terahertz analog applications

Vanadium dioxide (VO2), with its characteristic metal-insulator phase transition, is a prospective active candidate to realize tunable optical devices operating at terahertz (THz) frequencies. However, the abrupt phase transition restricts its practical use in analog-like continuous applications. Incorporation of tungsten is a feasible approach to alter the phase transition properties of thin VO2 films. We show that amplitude THz modulation depth of ∼65%, characteristic phase transition temperature of ∼40 °C, and tuning range larger than 35 °C can be achieved with W-doped VO2 films grown on sapphire substrates. W-doped VO2 films can also be used to suppress Fabry-Perot resonances at THz frequencies but at temperatures much lower than that observed for undoped VO2 films. The gradual phase transition temperature window allows for precise control of the W-doped VO2 optical properties for future analog based THz devices.

Force-induced globule-coil transition in laminin binding protein and its role for viral-cell membrane fusion.

The specific interactions of the pairs laminin binding protein (LBP)-purified tick-borne encephalitis viral surface protein E and certain recombinant fragments of this protein, as well as West Nile viral surface protein E and certain recombinant fragments of that protein, are studied by combined methods of single-molecule dynamic force spectroscopy (SMDFS), enzyme immunoassay and optical surface waves-based biosensor measurements. The experiments were performed at neutral pH (7.4) and acid pH (5.3) conditions. The data obtained confirm the role of LBP as a cell receptor for two typical viral species of the Flavivirus genus. A comparison of these data with similar data obtained for another cell receptor of this family, namely human αVβ3 integrin, reveals that both these receptors are very important. Studying the specific interaction between the cell receptors in question and specially prepared monoclonal antibodies against them, we could show that both interaction sites involved in the process of virus-cell interaction remain intact at pH 5.3. At the same time, for these acid conditions characteristic for an endosome during flavivirus-cell membrane fusion, SMDFS data reveal the existence of a force-induced (effective already for forces as small as 30-70 pN) sharp globule-coil transition for LBP and LBP-fragments of protein E complexes. We argue that this conformational transformation, being an analog of abrupt first-order phase transition and having similarity with the famous Rayleigh hydrodynamic instability, might be indispensable for the flavivirus-cell membrane fusion process.

Simplified lattice model for polypeptide fibrillar transitions.

Polypeptide fibrillar transitions are studied using a simplified lattice model, modified from the three-state Potts model, where uniform residues as spins, placed on a cubic lattice, can interact with neighbors to form coil, helical, sheet, or fibrillar structure. Using the transfer matrix method and numerical calculations, we analyzed the partition function and construct phase diagrams. The model manifests phase transitions among coil, helix, sheet, and fibril through parameterizing bond coupling energy ɛh,ɛs,ɛf, structural entropies sh,ss,sf of helical, sheet, and fibrillar states, and number density ρ. The phase diagrams show the transition sequence is basically governed by ɛh, ɛs, and ɛf, while the transition temperature is determined by the competition among ɛh, ɛs, and ɛf, as well as sh, ss, sf, and ρ. Furthermore, the fibrillation is accompanied with an abrupt phase transition from coil, helix, or sheet to fibril even for short polypeptide length, resembling the feature of nucleation-growth process. The finite-size effect in specific heat at transitions for the nonfibrillation case can be described by the scaling form of lattice model. With rich phase-transition properties, our model provides a useful reference for protein aggregation experiments and modeling.

Abrupt Phase Transition Based on Electron-transfer-coupled Spin Transition in a Cyanide-bridged [Co2Fe2] Tetranuclear Complex

Abstract A cyanide-bridged tetranuclear complex, [Co2Fe2(CN)6(tp*)2(dmbpy)4](PF6)2·4CH3CN (1·4CH3CN) (tp*: hydrotris(3,5-dimethylpyrazol-1-yl)borate and dmbpy: 5,5′-dimethyl-2,2′-bipyridine), was synthesized and its magnetic properties were investigated. Magnetic susceptibility measurements revealed that 1 exhibited an abrupt one-step thermal phase transition based on electron-transfer-coupled spin transition (ETCST) and light-induced ETCST at low temperature.

Two-dimensional nonautonomous solitons in parity-time symmetric optical media

An inhomogeneous nonlinear Schrödinger equation with diffraction and nonlinearity in the presence of the parity-time symmetric potential is studied, and 2D nonautonomous soliton family solutions are derived. The positive and negative signs in the phase bring about two kinds of abrupt phase transitions. Dynamical characteristics of form factors including the amplitude, width and phase are analyzed. The broadening and the compression of nonautonomous fundamental soliton are discussed. Moreover, the comparison of the dynamical behaviors of nonautonomous fundamental soliton in the diffraction decreasing waveguide with Gaussian, Logarithmic and hyperbolic profiles is investigated.

Phase transitions in number theory: From the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed.