Spatial Correlation Length Research Articles

Study of oxygen transport in glassy polymers on a nanometer length scale utilizing the kinetic Monte Carlo simulations.

Diffusion-controlled deactivation of excited phenanthrene and oxidation of triplet aryl-nitrene by molecular oxygen were used to determine the energetics of oxygen jump rates in the set of glassy polymers: poly(methyl methacrylate), poly(n-butyl methacrylate), polycarbonate, polystyrene, and polysulfone. To interpret experimental results, a simple model based on the transition state theory of diffusion jump has been used. The kinetic Monte Carlo simulations of phenanthrene deactivation and nitrene oxidation were carried out in a cubic lattice that modeled a polymer matrix. The bonds of the lattice were assigned to be activation barriers for the diffusion jumps of oxygen molecules from one site of the lattice to another. The standard deviation, σ‡, and spatial correlation length, rc, of the free energy of diffusion jump have been determined. It is shown that the spatial correlation of oxygen jump rates on a nanometer scale and the entropic nature of the dynamic heterogeneity are common features of all the studied polymers.

Convolutional neural network-based regression analysis to predict subnuclear chromatin organization from two-dimensional optical scattering signals.

Azimuth-resolved optical scattering signals obtained from cell nuclei are sensitive to changes in their internal refractive index profile. These two-dimensional signals can therefore offer significant insights into chromatin organization. We aim to determine whether two-dimensional scattering signals can be used in an inverse scheme to extract the spatial correlation length and extent of subnuclear refractive index fluctuations to provide quantitative information on chromatin distribution. Since an analytical formulation that links azimuth-resolved signals to and is not feasible, we set out to assess the potential of machine learning to predict these parameters via a data-driven approach. We carry out a convolutional neural network (CNN)-based regression analysis on 198 numerically computed signals for nuclear models constructed with varying in steps of between 0.4 and , and varying in steps of 0.005 between 0.005 and 0.035. We quantify the performance of our analysis using a five-fold cross-validation technique. The results show agreement between the true and predicted values for both and , with mean absolute percent errors of 8.5% and 13.5%, respectively. These errors are smaller than the minimum percent increment between successive values for respective parameters characterizing the constructed models and thus signify an extremely good prediction performance over the range of interest. Our results reveal that CNN-based regression can be a powerful approach for exploiting the information content of two-dimensional optical scattering signals and hence monitoring chromatin organization in a quantitative manner.

Many-Body Entropies and Entanglement from Polynomially Many Local Measurements

Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms. Published by the American Physical Society 2024

Numerical analysis of hydrogen storage in lined rock cavern under high pressure and its implications to hydrogen embrittlement

Underground hydrogen storage could provide buffer capacity to store the excess energy from renewable resources. A lined rock cavern (LRC) is one of the hydrogen geologic storage site options. It offers great flexibility because it does not rely on the existence of salt caverns, aquifer formations or depleted hydrocarbon reservoir fields. However, many important aspects have to be investigated before its full-scale implementation, among them (1) the effect of spatial variation of rock mass properties and (2) hydrogen embrittlement on the steel lining. We present a numerical study on these two aspects by simulating field tests at a pilot LRC project. For the effect of rock heterogeneity, we assign a spatial variation of elastic properties based on the Gaussian covariance model. The results show a good agreement with the field measurements. The spatial correlation length of rock mass elastic properties only has a minor impact on the cavern surface deformation. Regarding hydrogen embrittlement, our simulations predict a significant hydrogen diffusion in the low alloy steel (S355) lining after ∼2 months of operation. The fracture simulations show little fracture propagation even after 10 years of contact with hydrogen gas. However, the product loss may be too high for the low alloy steel (S355). We would recommend the use of stainless steel to inhibit the hydrogen diffusion. We show that advanced numerical models are powerful tools to ensure the safety of hydrogen storage in LRCs.

Prediction of Regional Broadband Strong Ground Motions Using a Teleseismic Source Model of the 18 April 2014 Mw 7.3 Papanoa, Mexico, Earthquake

ABSTRACT To estimate predicted ground motion from a teleseismic slip model, we use a low- and high-frequency hybrid method to simulate the regional, strong ground motions observed following the 18 April 2014 moment magnitude (Mw) 7.3 Papanoa, Mexico, earthquake. To generate the regional ground motion at low frequencies (<1 Hz), a teleseismically derived, finite-fault, kinematic model is used to define the earthquake source, taking into account slip-model variations identified with a parameter sampling approach that considers possible errors in the fault geometry, the hypocenter depth, and the rupture velocity. A 3D crustal model is used to calculate the low-frequency ground motions using a finite-element calculation that includes topography and considers variations in the source model to estimate the uncertainty in the calculations. High frequencies (>1 Hz) are added using a 1D full-wave propagation code that estimates uncertainties by considering multiple random distributions of slip with different spatial correlation lengths. The synthetic, broadband (0.05–10.0 Hz) ground motions are obtained by combining the low- and high-frequency portions match filtered at 1 Hz. These synthetic ground motions are compared with the regional observations using velocity records, peak ground acceleration, and medians of the orientation-independent response spectra of the horizontal components (RotD50) calculated at periods of 0.2, 0.3, 0.5, 1.0, 2.0, 3.0, 5.0, 7.5, and 10.0 s. The results indicate that ground motions estimated at these periods using our hybrid approach based primarily on a teleseismically derived source model are comparable to the values observed for the 2014 Papanoa earthquake at regional distances. The approach could be used to estimate strong-motion spectral levels expected for regions with limited local and regional recordings and could also fill in magnitude or distance gaps in ground-motion prediction relations utilized in the assessment of seismic hazard.

Influence of the disorder correlation length on localization and quantum state transference in tight-binding channels

We investigate in detail the transference of quantum states in a disordered channel. We consider a one-dimensional tight-binding model consisting of a source S connected to a receiver R throughout a disordered channel. The disorder distribution contains a single tunable spatial correlation length. We demonstrate that the disorder correlation length plays a relevant role within the localization properties of the channel. The hopping parameter between the sites S and R and the channel are also adjustable parameters. We investigate the possibility of transference of quantum states along this quantum channel model and describe the optimal conditions for the occurrence of a high fidelity process.

Impact of rock heterogeneity on reactive flow during acid stimulation process

Acid stimulation within carbonate rocks represents a crucial aspect of reactive flow applications in subsurface porous media and has been widely used in carbonate reservoir development attributed to its rapid effectiveness and cost-efficiency. This study is motivated to investigate further the impact of rock heterogeneity on the acid stimulation process. The two-scale continuum model is employed for capturing mass, momentum, and energy transfer during the acid stimulation process. The core-scale model is expanded to consider the specific composition of solid minerals, including reactive minerals such as calcite and dolomite and non-reactive ones like quartz and clay. A heterogeneity generator is developed by coupling with the open-source geostatistical program to produce different heterogeneous parameters using random seeds with varying spatial correlation lengths. Sensitive cases are performed to present an investigation into the influence of mineral composition and matrix heterogeneity on the acid stimulation process. Results show that the typical results of acid stimulation are closely tied to different heterogeneity conditions. The optimum conditions for acid stimulation are sensitive to the concentration of reactive components. The optimum acid injection rate declines as dolomite content increases, while the corresponding acidizing breakthrough volume reduces with higher calcite levels. The presence of mineral layers, especially in horizontal distributions, complicates acid fluid efficiency due to the competitive reaction between calcite and dolomite. Compared to the heterogeneous distribution of minerals, matrix heterogeneity plays a critical role in acid fluid consumption efficiency. Increasing heterogeneity leads to significant reductions in breakthrough volumes, largely governed by the correlation length.

Mechanical anisotropy associated with beddings in shale under Brazilian test conditions: Insights from acoustic emission statistics

A comprehensive understanding of shale’s bedding anisotropy is crucial for shale-related engineering activities, such as hydraulic fracturing, drilling and underground excavation. In this study, seven Brazilian tests were conducted on shale samples at different bedding orientations with respect to the loading direction (0°, 45° and 90°) and the disc end face (0°, 45° and 90°). An acoustic emission (AE) system was employed to capture the evolution of damage and the temporal-spatial distribution of microcracks under splitting-tensile stress. The results show that the Brazilian tensile strength decreases with increasing bedding inclination with respect to the disc end face, while it increases with the angle between bedding and loading directions. Increasing the bedding inclination with respect to the end face facilitates the reduction in b value and enhances the shale’s resistance to microcrack growth during the loading process. Misalignment between the bedding orientation and the end face suppresses the growth of mixed tensile-shear microcracks, while reducing the bedding angle relative to the loading direction is beneficial for creating mixed tensile-shear and tensile cracks. The observed microscopic failure characteristics are attributed to the competing effects of bedding activation and breakage of shale matrix at different bedding inclinations. The temporal-spatial distribution of microcracks, characterized by AE statistics including the correlation dimension and spatial correlation length, illustrates that the fractal evolution of microcracks is independent of bedding anisotropy, whereas the spatial distribution shows a stronger correlation. The evolution features of correlation dimension and spatial correlation length could be potentially used as precursors for shale splitting failure. These findings may be useful for predicting rock mass instability and analyzing the causes of catastrophic rupture.

Supervised and unsupervised learning of (1+1) -dimensional even-offspring branching annihilating random walks

Machine learning (ML) of phase transitions (PTs) has gradually become an effective approach that enables us to explore the nature of various PTs more promptly in equilibrium and nonequilibrium systems. Unlike equilibrium systems, non-equilibrium systems display more complicated and diverse features because of the extra dimension of time, which is not readily tractable, both theoretically and numerically. The combination of ML and most renowned nonequilibrium model, directed percolation (DP), led to some significant findings. In this study, ML is applied to (1+1) -d, even offspring branching annihilating random walks (BAW), whose universality class is not DP-like. The supervised learning of (1+1) -d BAW via convolutional neural networks (CNN) results in a more accurate prediction of the critical point than the Monte Carlo (MC) simulation for the same system sizes. The dynamic exponent z and spatial correlation length correlation exponent ν⊥ were also measured and found to be consistent with their respective theoretical values. Furthermore, the unsupervised learning of (1+1) -d BAW via an autoencoder (AE) gives rise to a transition point, which is the same as the critical point. The latent layer of AE, through a single neuron, can be regarded as the order parameter of the system being properly re-scaled. Therefore, we believe that ML has exciting application prospects in reaction-diffusion systems such as BAW and DP.

Stochastic analysis of the seismic performance of sheet-pile walls supporting heterogeneous liquefiable ground

This paper presents the findings of a stochastic analysis conducted to evaluate the effects of the spatial soil variability and temporal base motion variability on the seismic response of sheet pile walls supporting liquefiable ground. A random finite element analysis is used to model the centrifuge experiment performed during the 2020 phase of the Liquefaction Experiments and Analysis Project (LEAP). The relative density of the main soil deposit in the LEAP-2020 experiments ranged from 50 to 75 %. In this study the spatial variability of each centrifuge model was determined from the inflight cone penetration tests (CPT) performed before the shaking phase in each experiment. The vertical spatial correlation length was directly determined from the CPT measurements, while the mean and coefficient of variation of the soil relative density were obtained from an empirical relationship correlating the cone tip resistance with the relative density. The variability observed in the achieved base motions for the LEAP-2020 centrifuge experiments was modeled by generating synthetic base motion time histories that matched the variability observed in the response spectra of the achieved base motions. The results obtained from this analysis shed light on the effects of the base motion variability and soil density on the excess pore pressure development and the triggering of soil liquefaction. It also provides an understanding on the sensitivity of the wall lateral displacement to such variabilities. The observed variability in the simulation response is compared with the variability observed in the centrifuge experiments. This comparison is used to evaluate the capability of the current numerical simulation tools in modeling the variability in the wall response.

Impact of transport model resolution and a priori assumptions on inverse modeling of Swiss F-gas emissions

Abstract. Inverse modeling is a widely used top-down method to infer greenhouse gas (GHG) emissions and their spatial distribution based on atmospheric observations. The errors associated with inverse modeling have multiple sources, such as observations and a priori emission estimates, but they are often dominated by the transport model error. Here, we utilize the Lagrangian particle dispersion model (LPDM) FLEXPART (FLEXible PARTicle Dispersion Model), driven by the meteorological fields of the regional numerical weather prediction model COSMO. The main sources of errors in LPDMs are the turbulence diffusion parameterization and the meteorological fields. The latter are outputs of an Eulerian model. Recently, we introduced an improved parameterization scheme of the turbulence diffusion in FLEXPART, which significantly improves FLEXPART-COSMO simulations at 1 km resolution. We exploit F-gas measurements from two extended field campaigns on the Swiss Plateau (in Beromünster and Sottens), and we conduct both high-resolution (1 km) and low-resolution (7 km) FLEXPART transport simulations that are then used in a Bayesian analytical inversion to estimate spatial emission distributions. Our results for four F-gases (HFC-134a, HFC-125, HFC-32, SF6) indicate that both high-resolution inversions and a dense measurement network significantly improve the ability to estimate spatial distribution of the emissions. Furthermore, the total emission estimates from the high-resolution inversions (351 ± 44 Mg yr−1 for HFC-134a, 101 ± 21 Mg yr−1 for HFC-125, 50 ± 8 Mg yr−1 for HFC-32, 9.0 ± 1.1 Mg yr−1 for SF6) are significantly higher compared to the low-resolution inversions (20 %–40 % increase) and result in total a posteriori emission estimates that are closer to national inventory values as reported to the UNFCCC (10 %–20 % difference between high-resolution inversion estimates and inventory values compared to 30 %–40 % difference between the low-resolution inversion estimates and inventory values). Specifically, we attribute these improvements to a better representation of the atmospheric flow in complex terrain in the high-resolution model, partly induced by the more realistic topography. We further conduct numerous sensitivity inversions, varying different parameters and variables of our Bayesian inversion framework to explore the whole range of uncertainty in the inversion errors (e.g., inversion grid, spatial distribution of a priori emissions, covariance parameters like baseline uncertainty and spatial correlation length, temporal resolution of the assimilated observations, observation network, seasonality of emissions). From the abovementioned parameters, we find that the uncertainty of the mole fraction baseline and the spatial distribution of the a priori emissions have the largest impact on the a posteriori total emission estimates and their spatial distribution. This study is a step towards mitigating the errors associated with the transport models and better characterizing the uncertainty inherent in the inversion error. Improvements in the latter will facilitate the validation and standardization of national GHG emission inventories and support policymakers.

Universal Dynamics of Rogue Waves in a Quenched Spinor Bose Condensate.

Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent β_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{β_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.

The percolating cluster is invisible to image recognition with deep learning

We study the two-dimensional site-percolation model on a square lattice. In this paradigmatic model, sites are randomly occupied with probability p; a second-order phase transition from a non-percolating to a fully percolating phase appears at occupation density pc , called percolation threshold. Through supervised deep learning approaches like classification and regression, we show that standard convolutional neural networks (CNNs), known to work well in similar image recognition tasks, can identify pc and indeed classify the states of a percolation lattice according to their p content or predict their p value via regression. When using instead of p the spatial cluster correlation length ξ as labels, the recognition is beginning to falter. Finally, we show that the same network struggles to detect the presence of a spanning cluster. Rather, predictive power seems lost and the absence or presence of a global spanning cluster is not noticed by a CNN with a local convolutional kernel. Since the existence of such a spanning cluster is at the heart of the percolation problem, our results suggest that CNNs require careful application when used in physics, particularly when encountering less-explored situations.

A Hall-Petch-like relationship linking nanoscale heterogeneity to yield stress of heterogeneous metallic glasses

Metallic glasses (MGs) undergo plastic deformation through shear transformation zones (STZs) at small deformations and shear banding at large deformations. The STZ mechanism is linked to microstructural heterogeneities, including nano-heterogeneities associated with atom clustering and their spatial distribution. Shear banding occurs due to the coalescence of STZs. In this study, we investigate the yielding behavior of heterogeneous MGs by varying the spatial correlation and standard deviation of local shear moduli associated with clustering atoms on the nanoscale. Using a mesoscale shear transformation zone (STZ) dynamics model, we compute the yielding strength and observe deformation behaviors associated with the formation and propagation of STZs. We propose a Hall-Petch-like relationship where the yield stress of the MG scales inversely with the square root of the spatial correlation length. Our results show that the yielding of MGs corresponds to the percolation of STZs from soft to hard regions. Prior to macroscopic yielding, the activated STZs tend to accumulate inside soft regions, forming a Super-STZ array, which is similar to the formation of dislocation pile-up at grain boundaries. We derive the stress concentration in the front of the Super-STZ using the Eshelby inclusion model and formulate a Hall-Petch-like equation to quantify the yield of MGs with the spatial correlation length and standard deviation of the nanoscale heterogeneity. Our results provide insights into the structure-property relationship of MGs and have important implications for the design of nanoscale MGs with tunable properties.

Impact of Soil Properties’ Spatial Correlation Lengths and Inclination on Permanent Slope Displacements Due to Earthquake Excitation

Natural disasters, when and where they occur, often cause serious social and economic consequences, which require an urgent solution to the problem. In particular, Greece, which is characterized by a complex geological structure and intense tectonic stress, has suffered and continues to suffer the consequences of such catastrophic phenomena. Among the various destructive phenomena recorded on the Earth’s surface, two of the most important problems are landslides and land subsidence. The above phenomena may cause, in addition to the serious case of loss of human life, a threat to the social and economic fabric affecting sustainability in general, i.e., the quality of life of an area (destruction of property, filling of reservoirs, blockage of streams and rivers, etc.). In fact, landslides are a phenomenon with enormous social and economic consequences, since apart from the financial burden due to the collapse of a technical project or the interruption of transportation, they are accompanied by the loss of human life. This research examines the stochastic characteristics of a slopes’ stability to investigate the variation range of permanent earthquake movements. More specifically, the influence of inclination as well as the lengths of the spatial correlation of ground are investigated. The method in the present study follows the development of arbitrary fields of soil properties, which follow the Gaussian distribution characterized by autocorrelation lengths lx and ly in the horizontal and vertical directions, respectively, mean value μ, standard deviation σ, and cross-correlation coefficients ρij. The estimation of permanent displacements is performed by the combination of the Local Average Subdivision algorithm and the FLAC software (Fast Lagrangian Analysis of Continua) used in the parametric investigation of this work. The results of this research showed that the spatial correlation of the properties has an important impact on the permanent displacements of slopes caused by strong earthquake excitations.

QCD mesonic screening masses using Gribov quantization

The screening masses of mesons provide a gauge invariant and definite order parameter of chiral symmetry restoration. Different mesonic correlation lengths for flavor non-singlets, at least up to NLO, are well-defined gauge invariant physical quantities calculated earlier using the perturbative resummation techniques. The NLO perturbative results match the available non-perturbative lattice QCD results at the high-temperature regime. We have studied the spatial correlation lengths of various mesonic observables using the non-perturbative Gribov resummation, both for quenched QCD and (2+1) flavor QCD. The study follows the analogies with the NRQCD effective theory, a well-known theory for studying heavy quarkonia at zero temperature.

Prediction of fluid flow in porous media by sparse observations and physics-informed PointNet

We predict steady-state Stokes flow of fluids within porous media at pore scales using sparse point observations and a novel class of physics-informed neural networks, called “physics-informed PointNet” (PIPN). Taking the advantages of PIPN into account, three new features become available compared to physics-informed convolutional neural networks for porous medium applications. First, the input of PIPN is exclusively the pore spaces of porous media (rather than both the pore and grain spaces). This feature diminishes required computer memory. Second, PIPN represents the boundary of pore spaces smoothly and realistically (rather than pixel-wise representations). Third, spatial resolution can vary over the physical domain (rather than equally spaced resolutions). This feature enables users to reach an optimal resolution with a minimum computational cost. The performance of our framework is evaluated by the study of the influence of noisy sensor data, pressure observations, and spatial correlation length.

Interplanetary scintillation observation and space weather modelling

Interplanetary scintillation (IPS) refers to random fluctuations in radio intensity of distant small-diameter celestial object, over time periods of the order of 1 s. The scattering and scintillation of emergent radio waves are ascribed to turbulent density irregularities transported by the ubiquitous solar wind streams. The spatial correlation length of density irregularities and the Fresnel radius of radio diffraction are two key parameters in determining the scintillation pattern. Such a scintillation pattern can be measured and correlated between multi-station radio telescopes on the Earth. Using the “phase-changing screen” scenario based on the Born approximation, the bulk-flow speed and turbulent spectrum of the solar wind streams can be extracted from the single-station power spectra fitting and the multi-station cross-correlation analysis. Moreover, a numerical computer-assisted tomography (CAT) model, iteratively fit to a large number of IPS measurements over one Carrington rotation, can be used to reconstruct the global velocity and density structures in the inner heliosphere for the purpose of space weather modelling and prediction. In this review, we interpret the underlying physics governing the IPS phenomenon caused by the solar wind turbulence, describe the power spectrum and cross correlation of IPS signals, highlight the space weather application of IPS-CAT models, and emphasize the significant benefits from international cooperation within the Worldwide IPS Stations (WIPSS) network.

Using 3D-printed fluidics to study the role of permeability heterogeneity on miscible density-driven convection in porous media

Miscible density-driven convection in porous media has important implications to the long-term security of geological carbon sequestration. Laboratory investigations of miscible density-driven convection in heterogeneous porous media have been greatly limited due to the challenge in constructing well-controlled heterogeneous permeability fields. In this study, three-dimensional (3D) printing was used to solve the challenge. Particularly, elementary sediment blocks were 3D printed to construct heterogeneous permeability fields having the desired mean, standard deviation, and spatial correlation length of permeability. A methanol-ethylene-glycol (MEG) solution was placed at the top of the permeability field to trigger miscible density-driven downward convection. Results showed that permeability heterogeneity caused noticeable uncertainty in the total MEG mass transferred into the permeability field, and the uncertainty increased with increasing correlation length of the permeability field. In a heterogeneous permeability field with a larger spatial correlation length, a larger effective vertical permeability is in general favorable for solute mass transfer into the underlying porous medium. Conversely, in a heterogeneous permeability field with a shorter spatial correlation length, a larger effective vertical permeability does not necessarily lead to a higher mass transfer rate. This is because mass transfer across the top boundary through miscible density-driven convection depends on the flow recirculation near the interface. A large effective vertical permeability does not necessarily lead to fast flow recirculation because the former is measured in the vertical direction whereas the latter depends more on the internally-connected, high-permeability streaks within the domain. The 3D-printed elementary sediment blocks can be re-distributed to construct another permeability field easily, which greatly reduces the experimental time and thus significantly increases the total number of experiments that can be conducted, thereby approaching the ergodicity requirement when a large number of random permeability fields is needed.

Hyperscaling of the correlation length, interfacial tension, and specific heat in two-dimensional and quasi-two-dimensional liquids.

The line tension of two immiscible liquids under two-dimensional and quasi-two dimensional conditions is calculated as a function of temperature, using mesoscale numerical simulations, finding that it decays linearly. The liquid-liquid correlation length, defined as the thickness of their interface, is also predicted as the temperature is varied, and it diverges as the temperature becomes close to the critical temperature. These results are compared with recent experiments on lipid membranes and good agreement is obtained. The scaling exponents of the line tension (μ) and the spatial correlation length (ν) with temperature are extracted, finding that they fulfill the hyperscaling relationship, μ=d-1ν, where d is the dimension. The scaling of specific heat with temperature of the binary mixture is obtained as well. This is the first report of the successful test of the hyperscaling relation between μ and ν for d = 2 and for the non-trivial case of quasi-two dimensions. This work can help to understand experiments that test properties of nanomaterials using simple scaling laws, without needing to know specific chemical details of those materials.