Arbitrary Mixture Research Articles

BMT independence

We introduce the notion of BMT independence, enabling the study of arbitrary mixtures of Boolean, monotone, and tensor independence and generalizing the notion of BM independence of J. Wysoczanski. pairwise independence relations are encoded through a directed graph, which in turn determines the way mixed moments must be computed. Corresponding Central and Poisson-Type Limit Theorems are provided along with an explicit construction to realize BMT independent random variables as bounded operators on the tensor product of Hilbert spaces.

Exact analytical solution of the Flory-Huggins model and extensions to multicomponent systems.

The Flory-Huggins theory describes the phase separation of solutions containing polymers. Although it finds widespread application from polymer physics to materials science to biology, the concentrations that coexist in separate phases at equilibrium have not been determined analytically, and numerical techniques are required that restrict the theory's ease of application. In this work, we derive an implicit analytical solution to the Flory-Huggins theory of one polymer in a solvent by applying a procedure that we call the implicit substitution method. While the solutions are implicit and in the form of composite variables, they can be mapped explicitly to a phase diagram in composition space. We apply the same formalism to multicomponent polymeric systems, where we find analytical solutions for polydisperse mixtures of polymers of one type. Finally, while complete analytical solutions are not possible for arbitrary mixtures, we propose computationally efficient strategies to map out coexistence curves for systems with many components of different polymer types.

Toward higher-spin symmetry breaking in the bulk

We present a new vacuum of the bosonic higher-spin gauge theory in d+1 dimensions, which has leftover symmetry of the Poincaré algebra in d dimensions. Its structure is very simple: the space-time geometry is that of anti–de Sitter space, while the only nonzero field is a scalar. The scalar extends along the Poincaré radial coordinate z and is shown to be linearly exact for an arbitrary mixture of its two Δ=2 and Δ=d−2 conformal branches. The obtained vacuum breaks the global higher-spin symmetry, leading to a broken phase that lives in the Minkowski space-time. Published by the American Physical Society 2024

Robust approximation rules for critical electric field of dielectric gas mixtures

A semi-analytic method for quickly approximating the density-reduced critical electric field for arbitrary mixtures of gases is proposed and validated. Determination of this critical electric field is crucial for designing and testing alternatives to SF6 for insulating high voltage electrical equipment. We outline the theoretical basis of the approximation formula from electron fluid conservation equations, and demonstrate how for binary mixtures the critical electric field can be computed from the transport data of electrons in the pure gases. We demonstrate validity of the method in mixtures of N2 and O2, and SF6 and O2. We conclude with an application of the method to approximate the critical electric field for mixtures of SF6 and HFO1234ze(E), which is a high interest mixture being actively studied for high voltage insulation applications.

Gaussian universality of perceptrons with random labels.

While classical in many theoretical settings-and in particular in statistical physics-inspired works-the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we redeem this line of work in the case of generalized linear classification, also known as the perceptron model, with random labels. We argue that there is a large universality class of high-dimensional input data for which we obtain the same minimum training loss as for Gaussian data with corresponding data covariance. In the limit of vanishing regularization, we further demonstrate that the training loss is independent of the data covariance. On the theoretical side, we prove this universality for an arbitrary mixture of homogeneous Gaussian clouds. Empirically, we show that the universality holds also for a broad range of real data sets.

Efficient Exploration of Adsorption Space for Separations in Metal-Organic Frameworks Combining the Use of Molecular Simulations, Machine Learning, and Ideal Adsorbed Solution Theory.

Adsorption-based separations using metal-organic frameworks (MOFs) are promising candidates for replacing common energy-intensive separation processes. The so-called adsorption space formed by the combination of billions of possible molecules and thousands of reported MOFs is vast. It is very challenging to comprehensively evaluate the performance of MOFs for chemical separation through experiments. Molecular simulations and machine learning (ML) have been widely applied to make predictions for adsorption-based separations. Previous ML approaches to these issues were typically limited to smaller molecules and often had poor accuracy in the dilute limit. To enable exploration of a wider adsorption space, we carefully selected a diverse set of 45 molecules and 335 MOFs and generated single-component isotherms of 15,075 MOF-molecule pairs by grand canonical Monte Carlo. Using this database, we successfully developed accurate (r2 > 0.9) machine learning models predicting adsorption isotherms of diverse molecules in large libraries of MOFs. With this approach, we can efficiently make predictions of large collections of MOFs for arbitrary mixture separations. By combining molecular simulation data and ML predictions with Ideal Adsorbed Solution Theory, we tested the ability of these approaches to make predictions of adsorption selectivity and loading for challenging near-azeotropic mixtures.

AL4GAP: Active learning workflow for generating DFT-SCAN accurate machine-learning potentials for combinatorial molten salt mixtures.

Machine learning interatomic potentials have emerged as a powerful tool for bypassing the spatiotemporal limitations of abinitio simulations, but major challenges remain in their efficient parameterization. We present AL4GAP, an ensemble active learning software workflow for generating multicomposition Gaussian approximation potentials (GAP) for arbitrary molten salt mixtures. The workflow capabilities include: (1) setting up user-defined combinatorial chemical spaces of charge neutral mixtures of arbitrary molten mixtures spanning 11 cations (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba and two heavy species, Nd, and Th) and 4 anions (F, Cl, Br, and I), (2) configurational sampling using low-cost empirical parameterizations, (3) active learning for down-selecting configurational samples for single point density functional theory calculations at the level of Strongly Constrained and Appropriately Normed (SCAN) exchange-correlation functional, and (4) Bayesian optimization for hyperparameter tuning of two-body and many-body GAP models. We apply the AL4GAP workflow to showcase high throughput generation of five independent GAP models for multicomposition binary-mixture melts, each of increasing complexity with respect to charge valency and electronic structure, namely: LiCl-KCl, NaCl-CaCl2, KCl-NdCl3, CaCl2-NdCl3, and KCl-ThCl4. Our results indicate that GAP models can accurately predict structure for diverse molten salt mixture with density functional theory (DFT)-SCAN accuracy, capturing the intermediate range ordering characteristic of the multivalent cationic melts.

Theory of adsorption of ethoxylates at the water | oil and water | air interfaces. 1. Monolayers of single-component and Poisson distributed alkylphenol ethoxylates

Currently, the bulk thermodynamic properties of an arbitrary liquid mixture of oligomers are accessible with reasonable accuracy through popular 3D statistical models (SAFT, Flory-Huggins) under a wide range of conditions. These models are implemented in widely available software suites used for process design. The hypothesis investigated here is that the same is, in principle, achievable with monolayers of mixed surfactants on liquid surfaces. A molecular thermodynamic theory of the adsorption of alkylphenoxypolyethoxyethanols, CnH2n+1C6H4(OC2H4)mOH, on fluid interfaces is presented. It covers homologues of m = 0–10; water|alkane and water|gas interfaces; single surfactants and surfactant mixtures. The adsorption behaviour has been predicted as a function of the structure of the ethoxylated surfactants and the model has been validated against tensiometric data for forty systems. All values of the adsorption parameters have been either predicted, independently determined, or at least compared to a theoretical estimate. The single surfactant parameters have been used to predict the properties of ‘normal’ Poisson distributed mixtures of ethoxylates, in good agreement with literature data. Partitioning between water and oil, micellization, solubility and surface phase transitions are also discussed.

Расчет и корректировка значений упругих свойств топливных смесей

The paper substantiates the use of a simple and convenient Cole equation form of state making it possible to quickly and with sufficient accuracy determine density, compressibility coefficient and speed of sound of the fuel mixtures at high and ultrahigh injection pressures. A method is described for calculating these elastic properties of the fuel mixtures using the constants of the state equation selected in the form of expressions that determine dependence of the constants on the temperature. Expediency of introducing the universal correction factors is shown, which allows refining calculated values of the fuel mixture elastic properties. Processed experimental data from the literature sources and conducted studies formed the basis to obtain empirical coefficients to determine the correction factors that are refining values of the arbitrary composition mixture properties. The described method and the found coefficients make it possible to hydrodynamically calculate the fuel supply process using modern mathematical models and to design new fuel systems with the higher injection parameters.

General estimation method for lower flammability limits of organic compounds: The simpler the better

Due to the lack of well-established procedures to estimate the lower flammability limit (LFL) of arbitrary fuel-air mixtures, we report therein a simple method derived from a relationship introduced over 80 years ago for C–H–O molecules and presently extended to molecules containing C–H–N–O–F–Cl–Br–I–Si–P–S elements. The LFL was usually found to represent a constant fraction α≃1/2 of the stoichiometric concentration of fuel, except for halogen compounds for which α increases with the fraction of halogen atoms in the fuel molecules. Interestingly, this extremely simple scheme, which could be then easily integrated into any molecule design workflow, indicates that LFL values are mainly determined by the element count on the fuel structure, in sharp contrast with the premises underlying quantitative structure–property relationship (QSPR) and group contribution (GC) approaches.

A theory for combinations of risk measures

We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation for resulting risk measures from the properties of both alternative functionals and combination functions. To that, we build on the development of a representation for arbitrary mixture of convex risk measures. In this case, we obtain a penalty that recalls the notion of inf-convolution under theoretical measure integration. As an application, we address the context of probability-based risk measurements for functionals on the set of distribution functions. We develop results related to this specific context. We also explore features of individual interest generated by our framework, such as the preservation of continuity properties, the representation of worst-case risk measures, stochastic dominance and elicitability. We also address model uncertainty measurement under our framework and propose a new class of measures for this task.

New laboratory procedure for distinguishing smectites with varying permanent layer charge based on the combination of Cu-trien and ethylene glycol solvation methods and X-ray diffraction

Permanent layer charge of smectites (or smectite layers in mixed-layer minerals) is important for their properties and materials' applicationss. However, distinguishing low- and high-charge smectites by traditional laboratory methods is time-consuming and instrumentally demanding and it can also produce equivocal results. In addition, the use of structural formulae based on chemical analyses combined with knowledge on crystallochemistry is challenging in arbitrary mineral mixtures. The aim of this work was to test a novel laboratory procedure for distinguishing actual multi-mineral specimens of smectites according to their permanent layer charge. This is conducted on interlayer cation exchange by the Cu-trien complex and subsequent solvation with ethylene glycol. This procedure returned more straightforward results than the traditional routine of ethylene glycol-saturated K+-exchanged specimens by producing better-resolved X-ray diffraction (XRD) patterns. The practical application was demonstrated by analysing sauconite samples from Skorpion in Namibia, which was shown to contain more sauconite phases of distinct crystallographic properties present in variable proportions. XRD of the oriented ethylene glycol-saturated specimens was insufficient for this purpose. The procedure was tested by reference clay minerals of the smectite group with varying structural parameters. It was distinguished more smectite phases with distinct layer charges and estimated the layer charge by combining interlayer cation exchange with the Cu-trien complex and ethylene glycol solvation. This was followed by XRD analyses and full-profile diffraction pattern modeling. Further investigation is required for comparison with other methods. Possible reasons for the formation of two populations of sauconites were discussed.

Calculation of the absorption coefficient of air at different heights using the HITRAN and ACE-FTS databases

Subject of study. Increasing requirements for the accuracy of modeling the brightness characteristics of the atmosphere at different heights motivate the development of more detailed methods for the calculation of the absorption coefficient of air. Method. Modern databases of satellite sounding of the atmosphere that contain information on the volume fractions of air components at different heights in combination with a database of the parameters of the spectral lines of gases can be used in this task to calculate the spectral absorption coefficient. The possibility of specifying the geographic position of the height profiles of the air components (by specifying latitude and longitude) is an additional advantage of using the databases of satellite sounding. This method enables the differences in air compositions above different regions of the Earth to be considered. These databases usually provide information starting from a certain height; thus, databases of satellite sounding must be combined with the data obtained either from ground-based meteorological stations or using model distributions. The ACE-FTS database was used in this study, and it was combined with the standard atmosphere MODTRAN models at low heights. A filter for the ACE-FTS database was implemented using C++. The HITRAN database was used to calculate absorption coefficients. The ACE-FTS database provides data for 43 components of air, and the HITRAN database contains data for line-by-line calculation for 27 of these components and data on spectral absorption cross-sections for the remaining 16 components. Main results. A program for the calculation of the absorption coefficient of a multicomponent gas mixture was developed using C++. A Voigt profile was used in the line-by-line calculation, the effects of pressure and temperature on the line shift were considered, and line broadening owing to the following processes was considered: self-broadening, broadening resulting from interaction with water and carbon dioxide molecules, and broadening owing to interaction with other components of the air. The software explicitly considers the isotopic composition of molecules, thus enabling the calculation of not only the air mixture but also an arbitrary mixture with specified isotopic composition, information on which is in the HITRAN database. Moreover, the data of the high-temperature version HITEMP are considered. Practical significance. The combination of the ACE-FTS and HITRAN databases enables the calculation of a detailed profile of the spectral absorption coefficient of air for the specified month, temperature at the surface of the Earth, and geographic latitude and longitude, thus increasing the information content of the input data for the calculation of the brightness and transmission of the atmosphere at different heights. The data readout rate (parsing) and calculation speed of the developed program and the program HAPI implemented using Python are compared.

New Tools to Generate Realistic Ice Floe Fields for Computational Models

Abstract Global warming has extensively transformed Arctic sea ice from continuous level-ice coverage to unconsolidated ice floe fields. Whilst the ice floes have a mixture of different sizes and their locations are randomly distributed, contemporary computational models lack effective methods to generate floe fields with such a natural pattern. This work introduces two original tools that can generate realistic ice floe fields for computational models. They are a sequential generator that sequentially handles ice floes one by one, and a genetic generator based upon a genetic algorithm. Demonstration of the tools is given, presenting samples of generating various shapes of floes and arbitrary mixtures of different shapes. Furthermore, an example is provided that combines the generated floe field with computational work modeling a ship transiting in ice floes. In addition, the source code of the tools is sharable to the public.

Superfluid transition temperature and fluctuation theory of spin-orbit- and Rabi-coupled fermions with tunable interactions

We obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit- and Rabi-coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions for tunable $s$-wave interactions. In the presence of Rabi coupling, we find that spin-orbit coupling enhances (reduces) the critical temperature in the BEC (BCS) limit. For fixed interactions, we show that spin-orbit coupling can convert a first-order (discontinuous) phase transition into a second-order (continuous) phase transition, as a function of Rabi coupling. We derive the Ginzburg-Landau free energy to sixth power in the superfluid order parameter to describe both continuous and discontinuous phase transitions as a function of spin-orbit and Rabi couplings. Lastly, we develop a time-dependent Ginzburg-Landau fluctuation theory for an arbitrary mixture of Rashba and Dresselhaus spin-orbit couplings at any interaction strength.

Inclusion of solvent polarizability in the modeling of ion-dipole mixtures within the mean spherical approximation (MSA)

The fluctuating polarization model of Høye and Stell [J. Chem. Phys. 72, 1597 (1980); J. Chem. Phys. 73, 461 (1980)] is introduced in the non-primitive mean spherical approximation (MSA) framework for an arbitrary mixture of hard spherical ions and polar polarizable solvent molecules. The thermodynamic properties are derived for this more realistic representation of an aqueous electrolyte. The obtained explicit formulas constitute a thermodynamically consistent set.

A unified diffuse interface method for the interaction of rigid bodies with elastoplastic solids and multi-phase mixtures

This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field, and an interface seeding method is employed to mediate the interface boundary conditions. The method is based on an existing multi-material diffuse interface method that is capable of handling an arbitrary mixture of fluids and elastoplastic solids. The underlying method is general and can be extended to a range of different applications including high-strain rate deformation in elastoplastic solids and reactive fluid mixtures. As such, the new method presented here is thoroughly tested through a variety of problems, including fluid–rigid body interaction, elastoplastic–rigid body interaction, and detonation–structure interaction. Comparison is drawn between both experimental work and previous numerical results, with excellent agreement in both cases. The new method is straightforward to implement, highly local, and parallelizable. This allows the method to be employed in three dimensions with multiple levels of adaptive mesh refinement using complex immersed geometries. The rigid body field can be static or dynamic, with the tangent of hyperbola interface capturing reconstruction method being used to keep the interface sharp in the dynamic case.

A general justification for hybrid functionals in DFT by means of linear response theory* *To the memory of Enrico Clementi, an outstanding human being; in recognition of his pioneering work in quantum chemistry and in tribute to his leadership and long-lasting accomplishments.

In the present work, resorting to linear response theory, we examine the plausibility of postulating Kohn–Sham (KS)-type equations which contain, by definition, an effective hybrid potential made up by some arbitrary mixture of local and non-local terms. In this way a general justification for the construction of hybrid functionals is provided without resorting to arguments based on the adiabatic connection, the generalized KS theory or the Levy’s constrained search (or its variations). In particular, we examine the cases of single-hybrid functionals, derived from non-local exchange and of double-hybrid functionals, emerging from non-local second-order expressions obtained from the KS perturbation theory. A further generalization for higher-order hybrid functionals is also included.

Estimating Inhalation Exposure Resulting from Evaporation of Volatile Multicomponent Mixtures Using Different Modelling Approaches.

In many professional and industrial settings, liquid multicomponent mixtures are used as solvents, additives, coatings, biocidal products, etc. Since, in all of these examples, hazardous liquids can evaporate in the form of vapours, for risk assessments it is important to know the amount of chemicals in the surrounding air. Although several models are available in legal contexts, the current implementations seem to be unable to correctly simulate concentration changes that actually occur in volatile mixtures and in particular in thin films. In this research, the estimation of evaporation rates is based on models that take into account non-ideal behaviour of components in liquids and backpressure effects as well. The corresponding system of differential equations is solved numerically using an extended Euler algorithm that is based on a discretisation of time and space. Regarding air dispersion of volatile components, the model builds upon one-box and two-box mass balance models, because there is some evidence that these models, when selected and applied appropriately, can predict occupational exposures with sufficient precision. That way, numerical solutions for a wide variety of exposure scenarios with instantaneous and continuous/intermittent application, even considering “moving worker situations”, can be obtained. A number of example calculations have been carried out on scenarios where binary aqueous solutions of hydrogen peroxide or glutaraldehyde are applied as a biocidal product to surfaces by wiping. The results reveal that backpressure effects caused by large emission sources as well as deviations from liquid-phase ideality can influence the shape of the concentration time curves significantly. The results also provide some evidence that near-/far-field models should be used to avoid underestimation of exposure in large rooms when small/medium areas are applied. However, the near-field/far-field model should not be used to estimate peak exposure assuming instantaneous application, because then the models tend to overestimate peak exposure significantly. Although the example calculations are restricted to aqueous binary mixtures, the proposed approach is general and can be used for arbitrary liquid multicomponent mixtures, as long as backpressure effects and liquid-phase non-idealities are addressed adequately.

Threshold Sooting Index of Sustainable Aviation Fuel Candidates from Composition Input Alone: Progress toward Uncertainty Quantification

A quantitative structure–property relationship model has been developed to predict the threshold sooting index (TSI) of arbitrary mixtures of aliphatic and aromatic hydrocarbons of known composition. The model employs contributions from eight molecular fragments plus a global shift and a penalty factor for naphthenic compounds. For each coefficient, the contributions were determined by a constrained regression to data from five different experimental campaigns, which were stitched together by setting the TSI of methylcyclohexane to 5 and the TSI of 1-methylnaphthalene to 100. Unique to this study; the TSI of 1,3,5-trimethylbenzene was restricted to the range of 54.7 and 63.1, which significantly constrains uncertainty. Within the composite training dataset, which contained 65 molecules and 124 data points, including simple mixtures, the model was found to match 95% of the data within 8.9 TSI. Validation of the model against n-butylcyclohexane, dimethylcyclooctane, and a six-component surrogate jet fuel shows prediction to be well within the 95-percentile confidence band of the experiment. This model is the first to integrate the linear blending rule for the TSI with a linear quantitative structure–property relationship model for the TSI, and the first time that referee controls have been applied to ensure that all datasets, experimental and modeled, are normalized to the same scale.