Quadruple Point Research Articles

Temperature-tunable topological zero-refraction acoustic metamaterials

Zero-refractive index metamaterials have a wide range of applications in directional transmission and wave-front shaping due to their unusual acoustic properties. However, for most given acoustic topological metamaterials, the operating frequency is relatively fixed and the effect of temperature on their topological properties is rarely considered. Therefore, temperature-controlled tunable topological zero-refraction acoustic metamaterials are proposed in this paper. Firstly, a metamaterial with quadruple degenerate Dirac-like points at the center of the Brillouin zone is constructed, and the influence of temperature on the Dirac-like points is analyzed. The results show that the topological bandgap frequency range is more sensitive to temperature. The existence of pseudospin-polarized edge state is demonstrated by analysing the band structure of supercells with different topological phase phonon crystal. The topological zero-refraction property of the edge states outcoupled into free space is numerically demonstrated, and the non-contact active control of their operating frequencies can be realized by temperature. This study can provide a corresponding reference for the intelligent control of near-zero refractive index acoustic topological materials in elastic wave collimation and acoustic communication.

Exact results of the one-dimensional repulsive Hubbard model

We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and thek-Λstring bound states at arbitrary driving fields, showing subtle differences in spin magnons and chargeη-pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice.

Kinetic study on the effect of ice nucleation and generation on methane hydrate dissociation below the quadruple point

Natural gas hydrates (NGHs) have captured worldwide attention because of its huge resources and high energy density. Deep depressurization by dropping the pressure below the quadruple point is recognized as a promising exploitation method. However, the impact of ice formation on NGHs dissociation within depressurization is still controversial. Thus, we examine the dissociative behavior of NGHs at low temperature below the quadruple point using a high-pressure reactor. It primarily focuses on how ice formation affects heat and mass transfer, as well as the kinetics of hydrate dissociation. The results indicate that during the hydrate dissociation process, liquid water initially transforms into metastable supercooled water, which then transitions to solid ice under external disturbance. Ice nucleation predominantly occurs in two locations: within the free water phase and on the surface of hydrate particles. A double-edged effect of ice on NGHs dissociation is observed: the latent heat released by ice nucleation and generation could accelerate the hydrate breakdown (positive effect), while the decrease in permeability along with the self-preservation effect from ice formation tends to inhibit the NGHs dissolution (negative effect). In addition, a higher pressure drawdown rate can accelerate both ice nucleation and formation, which in turn shortens the freezing induction time. The increase of water saturation (SA) and the decrease of hydrate saturation (SH) can significantly reduce the mining time and strengthen both the hydrate dissociation rate (QH) and gas production rate (QP). Therefore, hydrate sediments with higher SA or lower SH are more conductive to gas recovery of low-temperature NGHs deposits in permafrost regions.

Role of microstructure on the development of local orientation gradients in polycrystals

In this work, we study the relationship between slip localizations and local orientation gradients in a polycrystalline material. We employ a 3D spatially resolved crystal plasticity-based micromechanics technique that includes explicit intragranular slip band modeling, called SB-FFT (slip band fast Fourier transform). EBSD analysis reveals the development of slip localizations, with a rare few generating relatively large local orientation gradients in the neighboring grain. Our results find that several conditions need to be met simultaneously for large zone of intense orientation gradients to form within a grain and with this, offer an explanation for their scarcity. These conditions entail the localization of slip to a sufficient high intensity in the grain neighbor, the grain experiencing higher stress levels than the average stress of its nearest grain neighborhood, and a crystallographic orientation suitable for activating secondary slip under the stress field produced by the slip localization. Analysis of the 3D orientation distributions as they evolve in strain indicates that orientation gradient zones cause the distribution to become highly skewed, with the extreme tails extending further as strain increases. The numerical simulations with various grain neighborhoods show that this feature is, however, not a sufficient signature for such orientation gradients associated with slip localizations since triple junctions or quadruple points can also produce intragranular orientation gradients that have a similar impact on the grain orientation distribution. Last, comparison with several previously proposed slip transmission criteria indicates that this phenomenon is not relevant, contrary to current belief.

Coupling and characterization of a Si/SiGe triple quantum dot array with a microwave resonator

Abstract Scaling up spin qubits in silicon-based quantum dots is one of the pivotal challenges in achieving large-scale semiconductor quantum computation. To satisfy the connectivity requirements and reduce the lithographic complexity, utilizing the qubit array structure and the circuit quantum electrodynamics (cQED) architecture together is expected to be a feasible scaling scheme. A triple-quantum dot (TQD) coupled with a superconducting resonator is regarded as a basic cell to demonstrate this extension scheme. In this article, we investigate a system consisting of a silicon TQD and a high-impedance TiN coplanar waveguide (CPW) resonator. The TQD can couple to the resonator via the right double-quantum dot (RDQD), which reaches the strong coupling regime with a charge–photon coupling strength of g 0/(2π) = 175 MHz. Moreover, we illustrate the high tunability of the TQD through the characterization of stability diagrams, quadruple points (QPs), and the quantum cellular automata (QCA) process. Our results contribute to fostering the exploration of silicon-based qubit integration.

Topologically protected entanglement switching around exceptional points

The robust operation of quantum entanglement states is crucial for applications in quantum information, computing, and communications1–3. However, it has always been a great challenge to complete such a task because of decoherence and disorder. Here, we propose theoretically and demonstrate experimentally an effective scheme to realize robust operation of quantum entanglement states by designing quadruple degeneracy exceptional points. By encircling the exceptional points on two overlapping Riemann energy surfaces, we have realized a chiral switch for entangled states with high fidelity. Owing to the topological protection conferred by the Riemann surface structure, this switching of chirality exhibits strong robustness against perturbations in the encircling path. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a new way for the application of non-Hermitian physics in the field of quantum information.

Exploring global symmetry-breaking superradiant phase via phase competition.

Superradiant phase transitions play a fundamental role in understanding the mechanism of collective light-matter interaction at the quantum level. Here we investigate multiple superradiant phases and phase transitions with different symmetry-breaking patterns in a two-mode V-type Dicke model. Interestingly, we show that there exists a quadruple point where one normal phase, one global symmetry-breaking superradiant phase, and two local symmetry-breaking superradiant phases meet. Such a global phase results from the phase competition between two local superradiant phases and cannot occur in the standard Λ- and Ξ-type three-level configurations in quantum optics. Moreover, we exhibit a sequential first-order quantum phase transition from one local to the global again to the other local superradiant phase. Our study opens up a perspective of exploring multilevel quantum critical phenomena with global symmetry breaking.

Large room-temperature electrocaloric response achieved by tailoring the first-order orthorhombic-tetragonal phase transition in BaTiO3-based ferroelectric ceramics

The development of refrigeration technology has burgeoned in response to the challenges posed by global warming. Notably, electrocaloric materials have garnered significant attention for their potential in miniaturization and high efficiency. However, investigations into the electrocaloric response in proximity to orthorhombic-tetragonal phase transition in BaTiO3-based ferroelectric ceramics remain scarce. In this study, we employ a lead-free x(Ba0.7Sr0.3)TiO3-(1-x)Ba(Zr0.2Ti0.8)O3 polycrystalline ceramics fabricated through the solid-state reaction method. The comprehensive analysis includes elucidation of the phase structure, surface morphologies, dielectric properties, domain switching behavior, and the electrocaloric effect. Integrating these findings with the phase diagram unveils optimal adiabatic temperature change (ΔT) achieved within the quadruple point coexistence region. That is, the highest ΔT of 0.53 K is achieved for x = 0.4 ceramic, which is attributed to the increased entropy resulting from multiple polar phases. Remarkably, the highest ΔT of 0.3 K is attained in x = 0.6 ceramic under a low driving electric field of 30 kV/cm at room temperature, precisely within the orthorhombic-tetragonal transition temperature. The investigation underscores the efficacy of regulating the first-order orthorhombic-tetragonal phase transition to achieve exceptional electrocaloric responses at room temperature.

T–x diagrams for the CO2–H2O system: The importance of water content in CO2 transportation for carbon capture and storage

AbstractWhen water is present in a CO2 pipeline, corrosion or plugging can occur due to the formation of liquid water or gas hydrate, respectively. Understanding how corrosion and hydrate plugging can be avoided is important for enhanced oil recovery and carbon dioxide capture and storage processes. If the CO2 is sufficiently dried prior to transportation, the formation of these problematic free‐water phases can be avoided. In this work, isobaric T–x diagrams were developed from the P–T diagram for the CO2–H2O binary system. Pressures ranging from just below the lower quadruple point to above the lower critical end point were studied. These diagrams are meant to give the reader a better conceptual understanding of how the water composition in CO2–H2O mixtures will influence phases that form at different temperatures and pressures. The diagrams are analyzed from the perspective of flow assurance in CO2 transportation.

Defect-induced fracture topologies in Al2O3 ceramic-graphene nanocomposites

Models of ceramic-graphene nanocomposites are used to study how the manufacturing process-dependent arrangement of reduced graphene oxide (rGO) inclusions governs nano-crack network development. The work builds upon recent studies of such composites where a novel combinatorial approach was used to investigate the effect of rGO arrangements on electrical conductivity and porosity. This approach considers explicitly the discrete structure of the composite and represents it as a collection of entities of different dimensions - grains, grain boundaries, triple junctions, and quadruple points. Here, the combinatorial approach is developed further by considering the effects of rGO agglomerations, stress concentrators and adhesion energies on intergranular cracking. The results show that the fracture networks can be effectively controlled by the local ordering of rGO inclusions to allow for a concurrent increase in the strength and conductivity of the ceramic composites. It is shown that the ratio of local stress concentrators related to rGO inclusions and cracks is the most significant factor affecting the nano-crack network topology. The local spatial arrangement of rGO inclusions becomes an effective tool for controlling nano-crack network topology only when this ratio approaches one. It is anticipated that these results will inform future design of toughness-enhanced composites.

Evaluation of a Simplified Model for Three-Phase Equilibrium Calculations of Mixed Gas Hydrates

In this study, we perform an extensive evaluation of a simple model for hydrate equilibrium calculations of binary, ternary, and limited quaternary gas hydrate systems that are of practical interest for separation of gas mixtures. We adopt the model developed by Lipenkov and Istomin and analyze its performance at temperature conditions higher than the lower quadruple point. The model of interest calculates the dissociation pressure of mixed gas hydrate systems using a simple combination rule that involves the hydrate dissociation pressures of the pure gases and the gas mixture composition, which is at equilibrium with the aqueous and hydrate phases. Such an approach has been used extensively and successfully in polar science, as well as research related to space science where the temperatures are very low. However, the particular method has not been examined for cases of higher temperatures (i.e., above the melting point of the pure water). Such temperatures are of interest to practical industrial applications. Gases of interest for this study include eleven chemical components that are related to industrial gas-mixture separations. Calculations using the examined methodology, along with the commercial simulator CSMGem, are compared against experimental measurements, and the range of applicability of the method is delineated. Reasonable agreement (particularly at lower hydrate equilibrium pressures) between experiments and calculations is obtained considering the simplicity of the methodology. Depending on the hydrate-forming mixture considered, the percentage of absolute average deviation in predicting the hydrate equilibrium pressure is found to be in the range 3–91%, with the majority of systems having deviations that are less than 30%.

Non-equilibrium magnetic properties of a mixed spin (1/2, 1) Ising graphene nanoisland.

Based on Glauber-type stochastic dynamics intertwined with mean field theory, we have investigated a graphene nanoisland's out-of-equilibrium magnetic and thermomagnetic behaviors with a mixed ferrimagnetic spin (1/2, 1) configuration in the presence of an oscillating magnetic field. The influence of the oscillating external magnetic field, single-ion anisotropy and temperature on the dynamic magnetic properties (dynamic phase transitions, hysteresis loop areas, correlations, and phase diagrams) of the system is studied in detail. The results illustrate that single ion anisotropy and the magnetic field play important roles in the system's dynamic order parameters, phase transitions and phase diagrams. Dynamic phase diagrams display some dynamic special points such as dynamic tricritical points, quadruple points and some sort of reentrant phenomena, which strongly depend on interaction parameters. Our predicted results may provide a reference for future experimental and theoretical studies of the nanostructures.

Experimental study on metastable dissociation of sandy hydrate reservoirs

The depressurization method has been proven to be an energy-efficient and relatively feasible production technique for natural gas hydrates. However, during the depressurization process, especially when the hydrates reservoir approaches the quadruple point, it is inevitable to experience phenomena such as freezing and hydrates secondary formation. Therefore, most researchers think that the P-T near the quadruple point may not be suitable for the dissociation of hydrates and a series of depressurization control methods were adopted to avoid this. However, according to other researchers, the effect of depressurization near the quadruple point on the dissociation behavior of hydrates is not inhibitory, but even a promoting effect to a certain extent. In addition, A special region called metastable state appears with the decrease of pressure near the quadruple point, which makes the dissociation behavior of hydrate below the quadruple point different from that above it. Therefore, in this paper, to reveal more clearly the dissociation behavior of natural gas hydrates near the quadruple point and the influence of the existence of metastable state on the depressurization dissociation of hydrate, the dissociation experiment of natural gas hydrates in the porous medium peri-freezing point is investigated in different depressurization rates and amplitudes, peri-freezing point and pressure stabilization times quadruple point. Experimental studies have shown that the amount of dissociation of natural gas hydrates below the quadruple point is non-linearly correlated with the depressurization rate. This correlation is synergistically regulated by the depressurization magnitude per unit of time and the environmental heating efficiency. Compared with the dissociation of hydrates above the freezing point, the metastable region does not show an obvious inhibitory effect on the dissociation of hydrates, and it even effectively shortens the dissociation time of hydrates and improves the heat transfer efficiency of the reservoir. Under the dissociation pressure of 2.5 MPa (metastable state), the reservoir temperature rose from 0 °C to 1 °C in 2.9 h, 3.6 h less than that under 2.6 MPa (above the quadruple point), and 0.7 h more than that under 1.0 MPa (below the metastable state). In addition, the gas production rate of hydrates is improved when hydrates disengagement the metastable region, increasing by 65.12 % compared with those above the quadruple point. However, pressure stabilization times when hydrates are in a metastable state need to be kept within a certain interval, too long or short pressure stabilization time will inhibit the dissociation of hydrates, and reduce the promotion effect on the dissociation of hydrates.

SPATIAL AND STRUCTURAL COMPLEXITY OF CEREBRAL HEMISPHERES IN MALE AND FEMALE BRAIN: FRACTAL AND QUANTITATIVE ANALYSES OF MRI BRAIN SCANS

Objectives: The aim of the present study was to compare the features of the structural complexity of the cerebral hemispheres in men and women using fractal analysis of outlined and skeletonized images, as well as quantitative analysis of digital skeletons of the cerebral hemispheres. Material and Methods: Magnetic resonance imaging brain scans of 100 individuals aged 18-86 years (44 males and 56 females) were investigated. Five tomographic sections of each brain were selected for morphometric study (4 coronal and 1 axial sections). The sections were preprocessed, and outlined and skeletonized images were obtained. Fractal analysis was conducted using the two-dimensional box counting method, and fractal dimensions of outlined and skeletonized images were determined. Additionally, quantitative analysis of skeletonized images was performed, determining the following parameters: branches, junctions, end-point voxels, junction voxels, slab voxels, triple points, quadruple points, average branch length, and maximum branch length. Results: We observed that both variants of fractal dimension in males and females did not show significant differences, although most quantitative parameters in males were larger than those in females. Conclusions: The spatial and structural complexity of the cerebral hemispheres, as characterized by fractal dimensions, is almost indistinguishable between males and females. However, in some individual tomographic sections, the male brain may exhibit a slightly higher number of end-point voxels, corresponding to the gyri of the cerebral hemispheres. The obtained data can be used in clinical practice for diagnostic purposes (e.g., for detecting malformations) and for theoretical studies in neuroanatomy.

Solid-fluid phase behaviour in binary mixtures: A new classification focused on paraffinic systems

The solid-fluid phase behavior of mixtures is important in a variety of real situations of industrial interest, including paraffin precipitation from hydrocarbon reservoir fluids, supercritical extraction or precipitation processes, and cryogenic processes among others. In the case of binary mixtures with the presence of fluid and solid phases, such behaviors can yield different topologies in terms of critical lines, three-phase lines, critical end points and quadruple points. The classification proposed by Yamamoto et al. in 1989 for those topologies is probably the best known and most used one, besides being more complete than others when considering experimentally observed behaviors. Nevertheless, a number of publications and in particular two recent PhD theses developed in our groups, found other topologies which deviate from the types considered in Yamamoto's et al. classification. These two theses employed different modelling approaches, using equation of state models for describing fluid phases and differing essentially in considering each solid phase as either made of the heavy compound in pure state or made of a solid solution. The deviations from the types in Yamamoto's et al. classification are compiled and analyzed in this work. Moreover, a new classification is proposed for binary systems with varying degrees of asymmetry. Being motivated by the study of paraffin precipitation from reservoir fluids, this new classification, in contrast to Yamamoto's et al. classification, leaves out of consideration the lower temperature range (up to the triple point of the light component) while, on the other hand, it incorporates some possible behavior variations, in the temperature range of more practical interest, which are not accounted for in Yamamoto's et al. classification. The new classification is shown to cover all possible phase behavior evolutions in the binary series of methane or ethane or propane with a heavier n-alkane and also of carbon dioxide with a n-alkane, considering both, what is known so far in terms of experimental data, and some features predicted with different modelling approaches, which have not been confirmed yet at the experimental level.

A possible quadruple point in networks of directed networks under targeted attacks

Many real systems are known to interact with one another, forming networks of networks (NONs). Plenty of attention has been poured into the research on the robustness in NONs in the past decade. Previous studies focus on undirected networks, or directed networks under random attacks. While many real networks are directed and how networks of directed networks (NODNs) respond to targeted attacks remains unknown. We thus develop a general analytical tool for analyzing the robustness of NODNs under two kinds of targeted attacks: degree-based attacks and in-degree (out-degree)-based attacks. The analytical tool can perfectly predict the sizes of the final giant strongly connected components and the phase transitions on the NODNs in response to targeted attacks. By applying the tool to synthesis networks, we find that a quadruple point intersected by four different phase regions could appear in the random regular NODNs. To the best of our knowledge, it is the first time that a quadruple point is found in the studies of complex networks. In addition, we find triple points intersected by three phases in networks of directed scale-free networks, and critical points that connect two phases in networks of directed Erdös–Rényi networks. The discovery of these tipping points could help understand network robustness and enable better design of networked systems.

Dynamic behaviours of black hole phase transitions near quadruple points

Treating the horizon radius as an order parameter in a thermal fluctuation, the free energy landscape model sheds light on the dynamic behaviour of black hole phase transitions. Here we carry out the first investigation of the dynamics of the recently discovered multicriticality in black holes. We specifically consider black hole quadruple points in D = 4 Einstein gravity coupled to non-linear electrodynamics. We observe thermodynamic phase transitions between the four stable phases at a quadruple point as well as weak and strong oscillatory phenomena by numerically solving the Smoluchowski equation describing the evolution of the probability distribution function. We analyze the dynamic evolution of the different phases at various ensemble temperatures and find that the probability distribution of a final stationary state is closely tied to the structure of its off-shell Gibbs free energy.

Thermodynamically stable phases of asymptotically flat Lovelock black holes

We present the first examples of phase transitions in asymptotically flat black hole solutions. We analyse the thermodynamic properties of black holes in order Lovelock gravity, with zero cosmological constant. We find a new type of ‘inverted’ swallowtail indicative of stable temperature regions for an otherwise unstable neutral black hole, and demonstrate multiple such stable phases can exist and coexist at multi-critical points. We also find that for charged black holes, ordinary swallowtails can exist on the stable Gibbs free energy branch, allowing for multiple first order phase transitions as seen for anti-de Sitter (AdS) black holes. A triple point for N = 5 and a quadruple point for N = 7 are presented explicitly. We investigate changes in the Gibbs free energy as the lowest order Lovelock constant is varied, and draw comparisons to pressure changes for AdS black hole systems.

Direct Measurement of the Four-Phase Equilibrium Coexistence Vapor-Aqueous Solution-Ice-Gas Hydrate in Water-Carbon Dioxide System.

Precise data on the non-variant equilibrium of the four phases (vapor-aqueous solution-ice-gas hydrate) in P-T coordinates are highly desired for developing accurate thermodynamic models and can be used as reference points (similar to the triple point of water). Using the two-component hydrate-forming system CO2-H2O, we have proposed and validated a new express procedure for determining the temperature and pressure of the lower quadruple point Q1. The essence of the method is the direct measurement of these parameters after the successive formation of the gas hydrate and ice phases in the initial two-phase gas-water solution system under intense agitation of the fluids. After relaxation, the system occurs in the same equilibrium state (T = 271.60 K, P = 1.044 MPa), regardless of the initial parameters and the order of crystallization of the CO2 hydrate and ice phases. Considering the combined standard uncertainties (±0.023 K, ±0.021 MPa), the determined P and T values agree with the results of other authors obtained by a more sophisticated indirect method. Validating the developed approach for systems with other hydrate-forming gases is of great interest.

Multicritical phase transitions in Lovelock AdS black holes

We demonstrate that black holes in order $N\ensuremath{\ge}4$ Lovelock gravity can exhibit multicritical phase behavior. We show an explicit example of a quadruple point in $d=10$ fourth-order Lovelock gravity and a quintuple point in $d=14$ sixth-order Lovelock gravity. We also demonstrate that multicriticality can be realized for uncharged, nonrotating black holes by highlighting a new type of multicritical point between black holes and thermal radiation. We discuss the methodology used and make comparisons to other black hole multicritical points in terms of the Gibbs phase rule.