Two-dimensional Mixture Research Articles

Melting of binary mixtures

The melting process of two-dimensional binary mixtures is studied using the Langevin simulation method. The melting point of each component in a binary mixture is determined by the local relative interparticle distance fluctuation method. The results show that, compared with the monodisperse system, the components of the binary mixture exhibit a multi-step melting characteristic. Further, the melting process of binary mixtures is found to depend on the mixing ratio and charge ratio. It is shown that particle hopping motion plays a key role in understanding melting in binary mixtures.

Transport of topological defects in a biphasic mixture of active and passive nematic fluids

Collectively moving cellular systems often contain a proportion of dead cells or non-motile genotypes. When mixed, nematically aligning motile and non-motile agents are known to segregate spontaneously. However, the role that topological defects and active stresses play in shaping the distribution of the two phases remains unresolved. In this study, we investigate the behaviour of a two-dimensional binary mixture of active and passive nematic fluids to understand how topological defects are transported between the two phases and, ultimately, how this leads to the segregation of topological charges. When the activity of the motile phase is large, and the tension at the interface of motile and non-motile phases is weak, we find that the active phase tends to accumulate +1/2 defects and expel −1/2 defects so that the motile phase develops a net positive charge. Conversely, when the activity of the motile phase is comparatively small and interfacial tension is strong, the opposite occurs so that the active phase develops a net negative charge. We then use these simulations to develop a physical intuition of the underlying processes that drive the charge segregation. Lastly, we quantify the sensitivity of this process on the other model parameters, by exploring the effect that anchoring strength, orientational elasticity, friction, and volume fraction of the motile phase have on topological charge segregation. As +1/2 and −1/2 defects have very different effects on interface morphology and fluid transport, this study offers new insights into the spontaneous pattern formation that occurs when motile and non-motile cells interact.

Quantum Droplets in Two-Dimensional Bose Mixtures at Finite Temperature.

We investigate the formation of quantum droplets at finite temperature in attractive Bose mixtures subject to a strong transverse harmonic confinement. By means of exact path-integral MonteCarlo methods we determine the equilibrium density of the gas and the liquid as well as the pressure vs volume dependence along isothermal curves. Results for the equation of state and for the gas-liquid coexistence region in quasi-2D configurations are compared with calculations in strictly two dimensions, finding excellent agreement. Within the pure 2D model we explore the relevance of the quantum scale anomaly and we determine the critical interaction strength for the occurrence of the first-order gas to liquid transition. Furthermore, we find that the superfluid response develops suddenly, following the density jump from the gas to the liquid state.

BPT-PLR: A Balanced Partitioning and Training Framework with Pseudo-Label Relaxed Contrastive Loss for Noisy Label Learning.

While collecting training data, even with the manual verification of experts from crowdsourcing platforms, eliminating incorrect annotations (noisy labels) completely is difficult and expensive. In dealing with datasets that contain noisy labels, over-parameterized deep neural networks (DNNs) tend to overfit, leading to poor generalization and classification performance. As a result, noisy label learning (NLL) has received significant attention in recent years. Existing research shows that although DNNs eventually fit all training data, they first prioritize fitting clean samples, then gradually overfit to noisy samples. Mainstream methods utilize this characteristic to divide training data but face two issues: class imbalance in the segmented data subsets and the optimization conflict between unsupervised contrastive representation learning and supervised learning. To address these issues, we propose a Balanced Partitioning and Training framework with Pseudo-Label Relaxed contrastive loss called BPT-PLR, which includes two crucial processes: a balanced partitioning process with a two-dimensional Gaussian mixture model (BP-GMM) and a semi-supervised oversampling training process with a pseudo-label relaxed contrastive loss (SSO-PLR). The former utilizes both semantic feature information and model prediction results to identify noisy labels, introducing a balancing strategy to maintain class balance in the divided subsets as much as possible. The latter adopts the latest pseudo-label relaxed contrastive loss to replace unsupervised contrastive loss, reducing optimization conflicts between semi-supervised and unsupervised contrastive losses to improve performance. We validate the effectiveness of BPT-PLR on four benchmark datasets in the NLL field: CIFAR-10/100, Animal-10N, and Clothing1M. Extensive experiments comparing with state-of-the-art methods demonstrate that BPT-PLR can achieve optimal or near-optimal performance.

Magnetoroton in a two-dimensional Bose-Bose mixture

Magnetoroton in a two-dimensional Bose-Bose mixture

Quantum Monte Carlo and perturbative study of two-dimensional Bose-Fermi mixtures

Quantum Monte Carlo and perturbative study of two-dimensional Bose-Fermi mixtures

Numerical generation and verification of a two-dimensional virtual asphalt mixture

This paper aims at finding a robust method to generate a two-dimensional virtual asphalt mixture and to verify the suitability of the generated virtual mixture. First, three methods namely stereological method, Walraven formula and phase separation method are adopted to convert the actual three-dimensional gradation curves into two-dimensional ones. Then, an approach called semi whole scale cross section (SWSCS) method is developed to verify the results obtained and to determine the most robust procedure to follow. Third, the numerical two-dimensional geometry shape data library (GSDL) of different aggregates and voids and a robust method to assemble representative volume elements (RVEs) are developed using Matlab. Finally, a gradation curve from the literature is considered to generate a virtual asphalt mixture specimen, which is then imported in the finite element (FE) software Abaqus to simulate the dynamic modulus test. The virtual test results are further verified using available literature and another homogenization numerical prediction method based on the Mori-Tanaka's approach. The results show that the phase separation method is effective to convert the three-dimensional gradation curve to a two-dimensional one. The simulation results of the virtual asphalt mixture developed in this study turn out to be in good agreement with both previously presented literature data and Mori-Tanaka's theory.

OSCAA: A two-dimensional Gaussian mixture model for copy number variation association analysis.

Copy number variants (CNVs) are prevalent in the human genomeand are found to havea profound effect on genomic organization and human diseases. Discovering disease-associated CNVs is critical for understanding the pathogenesis of diseases and aiding their diagnosis and treatment. However, traditional methods for assessing the association between CNVs and disease risks adopt a two-stage strategy conducting quantitative CNV measurements first and then testing for association, which may lead to biased association estimation and low statistical power, serving as a major barrier in routine genome-wide assessment of such variation. In this article, we developed One-Stage CNV-disease Association Analysis(OSCAA), a flexible algorithm to discover disease-associated CNVs for both quantitative and qualitative traits. OSCAA employs a two-dimensional Gaussian mixture model that is built upon the PCs from copy number intensities, accounting for technical biases in CNV detection while simultaneously testing for their effect on outcome traits. In OSCAA, CNVs are identified and their associations with disease risk are evaluated simultaneously in a single step, taking into account the uncertainty of CNV identification in the statistical model. Our simulations demonstrated that OSCAA outperformed the existing one-stage method and traditional two-stage methods by yielding a more accurate estimate of the CNV-disease association, especially for short CNVs or CNVs with weak signals. In conclusion, OSCAA is a powerful and flexible approach for CNV association testing with high sensitivity and specificity, which can be easily applied to different traits and clinical risk predictions.

Stokes-Einstein relation for binary mixtures

The applicability of the Stokes-Einstein (SE) relation in two-dimensional finite binary mixtures is tested using the Langevin simulation method. Calculations of viscosity and self-diffusion coefficients are compared between monodisperse and binary systems. It is shown that adapted definitions of coupling strength Γ and screening parameter κ allow to describe the transport properties for both monodisperse and binary systems consistently. Further, it is discussed how the mixing ratio and charge ratio of the binary mixture affects transport properties.

A novel two-dimensional continuum mixture theory model for paraffin wax melting in a cavity heating from side considering volume change

Paraffin wax presents a considerable potential for thermal storage technologies, given its high latent heat. Therefore, the accurate and systematic modeling of its melting process bears significant importance. Yet, existing mathematical models fail to adequately address the velocity driven by the density change during the melting process. In this research, we introduce a novel model for paraffin wax melting within a square enclosure subject to side heating. Unlike current models, our approach posits that flow within the mushy zone is dictated by the mass equation, not Darcy’s equation, and thus excludes the usage of mushy zone constant. This assumption, premised on the idea that the density-deviation-driven flow precludes the bulk flow from penetrating the mushy zone, is confirmed through a carefully designed visual experiment. Utilizing our melting model, we construct a mathematical model anchored in the continuum mixture theory. Through a comparative analysis of results acquired by numerical methods and experimental data, we find that our innovative mathematical model effectively predicts real-world scenarios with remarkable precision. Furthermore, we explore the influence of flows within the mushy zone on the melting process. Our findings indicate a significant deviation in results when assuming zero velocity in the mushy zone, suggesting that the density-deviation-driven flow is numerically negligible. However, it is crucial to note the physical relevance of the density-deviation-driven flow in accurately predicting the melting process. The absence of this consideration allows the bulk flow in the liquid region to permeate the mushy zone, thereby introducing substantial errors.

Dynamical self-trapping of two-dimensional binary solitons in cross-combined linear and nonlinear optical lattices.

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the x direction for the first component and a 1D nonlinear optical lattice (NOL) in the y direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the y direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the y direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.

Quartet Superfluid in Two-Dimensional Mass-Imbalanced Fermi Mixtures.

Quartet superfluid (QSF) is a distinct type of fermion superfluidity that exhibits high-order correlation beyond the conventional BCS pairing paradigm. In this Letter, we report the emergent QSF in 2D mass-imbalanced Fermi mixtures with two-body contact interactions. This is facilitated by the formation of a quartet bound state in vacuum that consists of a light atom and three heavy fermions. For an optimized heavy-light number ratio 3:1, we identify QSF as the ground state in a considerable parameter regime of mass imbalance and 2D coupling strength. Its unique high-order correlation can be manifested in the momentum-space crystallization of a pairing field and density distribution of heavy fermions. Our results can be readily detected in Fermi-Fermi mixtures nowadays realized in cold atoms laboratories, and meanwhile shed light on exotic superfluidity in a broad context of mass-imbalanced fermion mixtures.

Defect-mediated dynamics of coherent structures in active nematics

Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and its breakdown, defined by the presence of topological defects. In contrast, little is known about positional coherence, that is, whether there is an organization in the underlying fluid motion—despite this being both a prominent and an experimentally accessible feature. Here we characterize the organization of fluid motion in active nematics using the notion of Lagrangian coherent structures by analyzing experimental data of two-dimensional mixtures of microtubules and kinesin, as well as numerical data obtained from the simulation of the active nematodynamic equations. Coherent structures consist of moving attractors and repellers, which orchestrate complex motion. To understand the interaction of positional and orientational coherence, we analyse experiments and simulations and find that +1/2 defects move and deform the attractors, functioning as control centres for collective motion. Additionally, we find that regions around isolated +1/2 defects undergo high bending and low stretching/shearing deformations, consistent with the local stress distribution. The stress is the minimum at the defect, whereas high differential stress along the defect orientation induces folding. Our work offers a new perspective to describe and control self-organization in active fluids, with potential applications to multicellular systems. Active matter exhibits positional coherence in addition to the well-known orientational order. It is now shown that coherent structures in active nematics—made of dynamical attractors and repellers—form, move and deform, steered by topological defects.

Field-driven cluster formation in two-dimensional colloidal binary mixtures.

We study size- and charge-asymmetric oppositely charged colloids driven by an external electric field. The large particles are connected by harmonic springs, forming a hexagonal-lattice network, while the small particles are free of bonds and exhibit fluidlike motion. We show that this model exhibits a cluster formation pattern when the external driving force exceeds a critical value. The clustering is accompanied with stable wave packets in vibrational motions of the large particles.

An analytical model for the velocity and gas fraction profiles near gas-evolving electrodes

Understanding multiphase flow close to the electrode surface is crucial to the design of electrolyzers, such as alkaline water electrolyzers for the production of green hydrogen. Vertical electrodes develop a narrow gas plume near their surface. We apply the integral method to the mixture model. Considering both exponentially varying and step-function gas fraction profiles, we derive analytical relations for plume thickness, velocity profile, and gas fraction near the electrode as a function of height and current density. We verify these analytical relations with the numerical solutions obtained using two-dimensional mixture model simulations. We find that for low gas fractions, the plume thickness decreases with an increase in current density for an exponentially varying gas fraction profile. In contrast, the plume thickness increases with increasing current density at high gas fractions for an approximately step-function-shaped gas fraction profile, in agreement with experiments from the literature.

Understanding the Two-Dimensional Mixing Behavior of 1-Naphthalenethiol and Octanethiol.

A two-dimensional (2D) mixture in the form of a self-assembled monolayer composed of two distinct organothiol compounds was created by sequentially depositing 1-naphthalenethiol (1NT) and octanethiol (OT) on a gold surface. By varying the sequence of deposition, two mixed surface systems were created. The surface structure of the resulting mixed monolayer was characterized with Scanning Tunneling Microscopy (STM) and showed surface disorder across all investigated domains. Elemental analysis was carried out with X-ray Photoelectron Spectroscopy (XPS) and indicated that the 1NT monolayer was prone to significant oxidation. Reductive desorption (RD) was used to characterize the binding strength and electrochemical environments of the molecular components in the mixture, and confirmed disordered molecular layers. Due to the presence of oxidized species in the 1NT monolayer, 1NT was displaced by OT resulting in a novel surface structure composed of either OT or 1NT. Monolayers of OT that were exposed to a solution of 1NT resulted in disordered surface structures with a significant amount of gold vacancy islands. To date, there is no experimental phase diagram explaining the chemical behavior of two-dimensional mixtures. This study addresses the need for an experimental understanding of the phase behavior of mixed organothiol self-assembled monolayers (SAMs).

Quantum-fluctuation-driven dynamics of droplet splashing, recoiling, and deposition in ultracold binary Bose gases

Droplet impact on a surface is practically relevant to a variety of fields in nature and industry, while a complete control of its outcomes remains challenging due to various unmanageable factors. In this work, we propose the quantum simulation of droplet impact outcomes in the platform of ultracold atoms. Specifically, we study the quantum-fluctuation-driven dynamics (QFDD) of two-dimensional Bose-Bose mixtures from an initial Townes soliton towards the formation of a quantum droplet. By tuning the fluctuation energy of the initial Townes state through its size and number, the subsequent QFDD can produce various outcomes including splashing, recoiling, and deposition, similar to those in droplet impact dynamics. We have utilized the Weber number to identify the thresholds of splashing and recoiling, and further established a universal scaling law between the maximum spreading factor and the Weber number in the recoiling regime. In addition, we show that the residual QFDD in the deposition regime can be used to probe the collective breathing modes of a quantum droplet. Our results reveal a mechanism for the droplet impact outcomes, which can be directly tested in cold-atom experiments and can pave the way for exploring intriguing droplet dynamics in a clean and fully controlled quantum setting.

An Extendable Gaussian Mixture Model for Lane-Based Queue Length Estimation Based on License Plate Recognition Data

Most existing studies on queue length estimation based on license plate recognition (LPR) data require multisection LPR data. Studies based on single-section LPR data cannot ensure the accuracy and stability of the estimates when missed detections occur, which greatly limits the practicability of existing studies. Therefore, using single-section LPR data, this study proposes a lane-based queue length estimation method based on a two-dimensional Gaussian mixture model. First, the LPR data were processed to obtain the departure times and time headway of vehicles. Then, the two-dimensional Gaussian distributions of queued vehicles and nonqueued vehicles were fitted, and the expectation-maximization algorithm was adopted to solve the distribution parameters. Finally, the queuing status of each vehicle was determined, and the lane-based queue length was estimated based on the last identified queued vehicle in the cycle. The empirical results showed that the mean absolute errors (MAEs) of the proposed method were just 1.3 veh/cycle under no missed detections and 2 veh/cycle under a 20% missed detection rate, outperforming existing methods. The simulation results indicate that the proposed method can achieve accurate estimates under various traffic demands. In addition, the proposed method can be extended to real-time applications and multisection LPR systems.

Dynamical excitation processes and correlations of three-body two-dimensional mixtures

A scheme is proposed to dynamically excite distinct eigenstate superpositions in three-body Bose-Fermi mixtures confined in a two-dimensional harmonic trap. The system is initialized in a non-interacting state with a variable spatial extent, and the scattering lengths are subsequently quenched. For spatial widths smaller than the three-body harmonic oscillator length, a superposition of trimers and atom-dimers is dynamically attained, otherwise trap states are predominantly populated. Accordingly, the Tan contacts evince the build-up of short range two- and three-body correlations in the course of the evolution. A larger spatial extent of the initial state leads to a reduction of few-body correlations, endowed however with characteristic peaks at the positions of the avoided-crossings in the energy spectra, thereby signalling the participation of atom-dimers. Our results expose ways to dynamically excite selectively trimers, atom-dimers and trapped few-body states characterized by substantial correlations and likely to be accessible within current experiments.

Gas-liquid interface of a Lennard-Jones binary mixture controlled by differential activity: phase transition and interfacial stability.

We perform molecular dynamics simulations of a two-dimensional binary mixture of Lennard-Jones particles, characterized by some degree of "activity" inside. Starting from a base state that features a gas-liquid interface and a completely segregated system at thermodynamic equilibrium, we introduce differential scalar activity between the two species by prescribing two different effective temperatures. The differential activity is measured as the ratio of the two temperatures. Previous studies showed segregation in a homogeneously mixed system induced by high activity. In this study, we investigate the effect of activity on a pre-existing gas-liquid interface between two separated species. Whereas a high activity ratio induces the formation of new interfaces, we show that a low activity ratio destabilizes existing ones. Moreover, the combination of a pre-existent interface with differential activity leads to partial crystallization and thus to triple phase coexistence (solid, liquid and gas), which is observed over a wide range of moderate differential activities. Findings from this idealized system can guide our understanding of interfacial behaviors in certain biological systems.