Universal Equation Research Articles

Modified Low-Field NMR Method for Improved Pore Space Analysis in Tight Fe-Bearing Siliciclastic and Extrusive Rocks

Abstract Understanding the filtration and storage properties of tight reservoirs is crucial for efficient resource exploitation, particularly in unconventional formations. This study presents two low-field nuclear magnetic resonance (LF-NMR) techniques: standard cut-off and modified differential approaches combined with mercury injection capillary pressure (MICP) and X-ray diffraction (XRD) studies to evaluate porosity and pore size distribution (PSD) in such formations. The differential technique involves subtracting the dry sample signal from a 100% water-saturated one, allowing the chemically bound water compound to be eliminated and facilitating PSD analysis. Through the application of the percolation theory, we established a power–law relationship between LF-NMR transverse relaxation time (T2) and MICP pore-throat diameter, enabling the derivation of PSD and pseudo capillary pressure curves. Our methodology was validated on a sample set representing tight sandstones, conglomerates, and extrusive rocks with high clay and iron mineral content, demonstrating the superior accuracy of the modified differential method in estimating effective porosity and absolute PSD in comparison with the standard approach. While the use of the percolation theory in PSD conversion was successful for rocks with unimodal distributions, it often failed for rocks with larger voids. The study also revealed that the relationship between the LF-NMR transverse relaxation times and MICP pore sizes is both nonlinear and challenging to describe with a universal equation, especially in the presence of para- and ferro-magnetic elements in the rock matrix. Despite obstacles to the complete elimination of the influence of these minerals on the T2 distribution, employing the modified differential LF-NMR method significantly mitigated this effect and offered a precise and noninvasive way of characterizing the petrophysical properties of tight reservoir rocks. Consequently, our studies offer a significant step toward a more precise assessment of pore structures in unconventional reservoirs that could be translated into more efficient strategies for locating geothermal heat and hydrocarbon resources.

Intrinsic Ferroelectric Switching in Two-Dimensional α-In2Se3.

Two-dimensional (2D) ferroelectric semiconductors present opportunities for integrating ferroelectrics into high-density ultrathin nanoelectronics. Among the few synthesized 2D ferroelectrics, α-In2Se3, known for its electrically addressable vertical polarization, has attracted significant interest. However, the understanding of many fundamental characteristics of this material, such as the existence of spontaneous in-plane polarization and switching mechanisms, remains controversial, marked by conflicting experimental and theoretical results. Here, our combined experimental characterizations with piezoresponse force microscope and symmetry analysis conclusively dismiss previous claims of in-plane ferroelectricity in single-domain α-In2Se3. The processes of vertical polarization switching in monolayer α-In2Se3 are explored with deep-learning-assisted large-scale molecular dynamics simulations, revealing atomistic mechanisms fundamentally different from those of bulk ferroelectrics. Despite lacking in-plane effective polarization, 1D domain walls can be moved by both out-of-plane and in-plane fields, exhibiting avalanche dynamics characterized by abrupt, intermittent moving patterns. The propagating velocity at various temperatures, field orientations, and strengths can be statistically described with a universal creep equation, featuring a dynamical exponent of 2 that is distinct from all known values for elastic interfaces moving in disordered media. This work rectifies a long-held misunderstanding regarding the in-plane ferroelectricity of α-In2Se3, and the quantitative characterizations of domain wall velocity will hold broad implications for both the fundamental understanding and technological applications of 2D ferroelectrics.

A universal yield stress equation for electrorheological fluids

In this study, we investigate the universality of the yield stress [τyE0, where E0 is electric field strength] for examining electrorheological (ER) fluids both experimentally and theoretically. We found that the published experimental data for the yield stress of ER fluids for various materials and measurement conditions obey a yield stress scaling equation. In other words, the ER yield stress data in the literature collapse onto a universal correlation: τ̂=1.313Ê3/2tanhÊ using scaled variables τ̂≡τyE0/τyEc and Ê≡E0/Ec. Here, Ec is critical electric field strength. Although this expression is attractive for experimentalists, this empirical equation has not been derived from first principles. We introduce a mesoscopic elementary region concept and justify this universal correlation for the first time. We decompose the ER system into a finite number of elementary regions and introduce “glueons,” which adhere to neighboring elementary regions resulting in fibrillary structures. We investigated the limiting case when the elementary region size is reduced to zero (continuum limit) and used a reaction-diffusion model to calculate glueon concentration. In modeling the reaction term (generation of glueons), we used a linear model by recognizing that the electric field activates glueons, i.e., the number of glueons increases as the electric field strength increases. In our preliminary study, we were able to justify a universal correlation by solving the glueon concentration equation using a simple geometry. The novelty of this work is the development of universality for the ER yield stress and derivation of a universal scaling equation.

Modeling the Dispersion of Waves in a Multilayered Inhomogeneous Membrane with Fractional-Order Infusion

The dispersion of elastic shear waves in multilayered bodies is a topic of extensive research due to its significance in contemporary science and engineering. Anti-plane shear motion, a two-dimensional mathematical model in solid mechanics, effectively captures shear wave propagation in elastic bodies with relative mathematical simplicity. This study models the vibration of elastic waves in a multilayered inhomogeneous circular membrane using the Helmholtz equation with fractional-order infusion, effectively leveraging the anti-plane shear motion equation to avoid the computational complexity of universal plane motion equations. The method of the separation of variables and the conformable Bessel equation are utilized for the analytical examination of the model’s resulting vibrational displacements, as well as the dispersion relation. Additionally, the influence of various wave phenomena, including the dependencies of the wavenumber on the frequency and the phase speed on the wavenumber, respectively, with the variational effect of the fractional order on wave dispersion is considered. Numerical simulations of prototypical cases validate the formulated model, illustrating its applicability and effectiveness. The study reveals that fractional-order infusion significantly impacts the dispersion of elastic waves in both single- and multilayer membranes. The effects vary depending on the membrane’s structure and the wave propagation regime (long-wave vs. short-wave). These findings underscore the potential of fractional-order parameters in tailoring wave behavior for diverse scientific and engineering applications.

Soil loss estimation using RUSLE model: Comparison of conventional and digital soil data at watershed scale in central Iran

Sustainable agriculture and eco-environment conservation face constant threats from soil erosion in mountainous regions. This study aimed to predict soil loss in the mountainous watershed by applying the Revise Universal Equation Soil Loss (RUSLE) and Sediment Delivery Ratio (SDR) models and to evaluate the efficacy of the RUSLE model through the observed data in a hydrometric station. Comparing a polygonal, and a digital soil map (prepared by the Kriging method) for deriving the K factor to estimate soil loss was another objective of the recent research. In this study, two scenarios were examined for the calculation of spatial variation of the K-factor; scenario I comprised soil data derived from a legacy soil map with eight soil units and the data from their representative soil profiles (i.e., traditional soil survey), and scenario II comprised K-factor derived from 100 studied sites using kriging technique (i.e., digital soil survey). The results of RUSLE modeling showed that there was no significant difference between scenario I (7.97 t/(ha. yr)) and scenario II (7.93 t/(ha. yr)) for predicting soil loss with the RUSLE model. This finding confirms that the RUSLE model with limited and legacy data can provide a reliable prediction of soil loss in the given watershed. Moreover, long and short-term periods were used to estimate soil loss, while in the long-term period, estimated soil loss had higher accordance with actual soil loss. Sediment delivery ratio was calculated using models of Vanoni, Boyce, USDA-SCS, and Slope-based models. The results indicated that the Slope-based model had the highest fitness (R2=0.946, ME=0.27, and RMSE=0.275 for scenario I and R2=0.9443, ME=0.26 and RMSE=0.40 for scenario II), with observed sedimentation rate at the hydrometric station at the outlet of the watershed. Overall, predicted soil loss severity map using the traditional soil map by RUSLE model could provide trustworthy information for decision makers and governors at the given and similar watersheds in semiarid regions.

Simplified Universal Equations for Ionic Conductivity and Transference Number

Nernst-Einstein equation can provide a reasonable estimate of the ionic conductivity of dilute solutions. For concentrated solutions, alternate methods such as Green–Kubo relations and Einstein relations are more suitable to account for ion-ion interactions. Such computations can be expensive for multicomponent systems. Simplified mathematical expressions like the Nernst-Einstein equation do not exist for concentrated multicomponent mixtures. Newman’s treatment of multicomponent concentrated solutions yields a conductivity relation in terms of species concentration and Onsager phenomenological coefficients. However, the estimation of these phenomenological coefficients is not straightforward. Here, mathematical formulations that relate the phenomenological coefficients with the friction coefficients are developed, leading to simplified, ready-to-use expressions of conductivity and transference numbers that can be used for a wide range of ionic mixtures. This approach involves spectral decomposition of the matrix of Onsager phenomenological coefficients. The general analytical expressions for conductivity and transference number are simplified for binary electrolytes, and numerical solutions are provided for ternary and quaternary mixtures with ion dissociation.

Estimación de la erosión en un área de deforestación en la cuenca amazónica del bajo río Acre

The Lower Acre River Basin is located in an area of deforestation with the implementation of pastures for beef cattle ranching in soils susceptible to erosion and equatorial climate. The existence of slaughterhouses and beef cattle in the municipality of Boca do Acre, in the state of Amazonas, is one of the problems linked to deforestation in the Brazilian Amazon. Given this scenario, an estimate of soil losses was presented with the application of the Universal Equation in a geographic information system. In the methodology, a database was elaborated with vectorized information for the extraction of the areas of the types of soils and land cover, including the spatial analysis of slopes extracted from the digital elevation model. Due to the analysis of the areas by geoprocessing occurring by vectorization, the calculations of the erosion plots were obtained through tables with the parameters adopted by the scientific references. It was found that 60% of the soil loss occurs in the area of agriculture in 11% of the territory of the watershed, being predominantly in areas of rural settlements of the state of Acre. As a result of the estimate, soil loss in the Lower Acre River Basin was 386,422 t/ha/year, with a production of 46 million tons of sediment per year.

Mean airway pressure - Minute ventilation product (mM): A simple and universal surrogate equation to calculate mechanical power in both volume and pressure controlled ventilation

Introduction Mechanical power represents the energy delivered by a mechanical ventilator onto the lungs. It incorporates all the variables participating in ventilator-induced lung injury, including driving pressure, tidal volume, positive end expiratory pressure, and respiratory rate. The pitfall of mechanical power is its mathematical complexity, as the gold standard method of calculation involves deriving the inspiratory area under the pressure-volume curve of each breath. Prior studies attempted to create simplified equations, they lack clinical utility as calculations cannot be done by solely looking at ventilator settings or they require manipulation of variables. There are also different formulas depending on the type of the mode of ventilation used. This study offers a simplified, universal equation called the mean airway pressure - Minute ventilation product (mM equation) which renders mechanical power clinical application more feasible at the bedside. Methods and Statistics Data collection used the online SIVA simulator, which simulate mechanical ventilation and calculate the geometrical area of the inspiratory limb of the pressure-volume curve. Different combinations of passive scenarios with varying compliances (10-80 ml/cmH2O) and resistances (5-30 cmH2O/L/S) in each the VCV and PCV modes were accomplished by adjusting ventilator settings with respiratory rate (5-40 BPM), tidal volume (150-700 mL), DP (5-30 cmH2O), and PEEP (0-15 cmH2O), with different inspiratory times in PCV and different flows rates in the VCV. A total of 2,000 values were collected in each mode. Range of Mechanical power measured by the simulator: 0.1 - 105 J/min and range of mM equation (mean airway pressure x Minute ventilation): 0.37 - 820 cmH2O/L/min. Pearson correlation coefficients were calculated to compare the relationship of the mM equation to the measured MP, and linear regressions were used for predicting the MP derived from the mM equation in each mode separately and when combining all data from both modes. T-test for equal variance and Bland Altmann plot were used to compare the reference MP measured (MPR) from the simulator to the one derived from the Mm formula (MPD). Results There was a statistically significant linear relationship (P < 0.001) and strong correlation of determination (R2 = 0.931), CI (0.961, 0.967) between the mM formula and the gold-standard method of calculating mechanical power for the combined two modes. For the VCV: there was a statistically significant linear relationship (P < 0.001) and strong correlation of determination (R2 = 0.936), CI (-0.963, 0.971). For the PCV: there was a statistically significant linear relationship (P < 0.001) and strong correlation of determination (R2 = 0.936), CI (-0.964, 0.970). A linear regression model predicted the MP from the mM as follows: for both modes MP = 0.13 (mM) + 3.41, for PCV MP = 0.15 (mM) + 3.79, for VCV MP = 0.13 (mM) + 2.48. The derived mechanical power from the mM was not statistically different (P 0.498) from the calculated reference MP using two sample T-tests assuming equal variance. The Bland-Altman plot for VCV mode showed a mean of 0.78 with 95% CI (0.34, 1.22), SD (-13.27, 14.83). In PCV, a mean of - 0.53 with 95% CI (-0.68, -0.38), SD (-6.28, 5.22). For both modes, a mean of 0, with 95% CI (-0.2, 0.2), SD (-10.06, 10.05). Conclusion The mM equation and its MP derived formula is a reliable method of calculating mechanical power. The simplicity and universal nature of its calculation can provide significant clinical utility at the bedside. More studies are needed to validate this method of calculation. Keywords: Mechanical power, mean airway pressure, minute ventilation

Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media

We theoretically investigate the scaling behavior of the localization length for s-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro–Loginov formula of differentiation, we accurately compute the localization length ξ of s waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter σ2 and the disorder correlation length lc. Away from the critical angle, ξ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber k, kξ depends on the single parameter klcσ2, satisfying a universal equation kξ≈1.3717klcσ2−1/3 across the entire range of parameter values. Additionally, we find that ξ scales as λ4/3 for the entire range of the wavelength λ, regardless of the values of σ2 and lc. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence.

Quantifying the accuracy of steady states obtained from the universal Lindblad equation

Quantifying the accuracy of steady states obtained from the universal Lindblad equation

The Effect of Temperature on the London Dispersive and Lewis Acid-Base Surface Energies of Polymethyl Methacrylate Adsorbed on Silica by Inverse Gas Chromatography

Inverse gas chromatography at infinite dilution was used to determine the surface thermodynamic properties of silica particles and PMMA adsorbed on silica, and more particularly, to quantify the London dispersive energy γsd, the Lewis acid γs+, and base γs− polar surface energies of PMMA/silica composites as a function of the temperature and the recovery fraction θ of PMMA. The polar acid-base surface energy γsAB and the total surface energy of the different composites were then deduced as a function of the temperature. In this paper, the Hamieh thermal model was used to quantify the surface thermodynamic energy of polymethyl methacrylate (PMMA) adsorbed on silica particles at different recovery fractions. A comparison of the new results was carried out with those obtained by applying other molecular models of the surface areas of organic molecules adsorbed on the different solid substrates. An important deviation of these molecular models from the thermal model was proved. The determination of γsd, γs+, γs−, and γsAB of PMMA in both the bulk and adsorbed phases showed an important non-linearity variation of these surface parameters as a function of the temperature. The presence of maxima in the curves of γsd(T) highlighted the second-order transition temperatures in PMMA showing beta-relaxation, glass transition, and liquid–liquid temperatures. These three transition temperatures depended on the adsorption rate of PMMA on silica. The proposed method gave a new relation between the recovery fraction of PMMA and its London dispersive energy, showing an important effect of the temperature on the surface energy parameters of the adsorption of PMMA on silica. A universal equation relating γsd(T,θ) of the systems PMMA/silica to the recovery fraction and the temperature was proposed.

Influence of solvent quality on the swelling and shear modulus of polymer gels chemically cross-linked in solution

The effect of temperature (T) is studied on the swelling of model poly(vinyl acetate) (PVAc) gels in isopropyl alcohol. The theta temperature Θ of these gels, at which the second osmotic virial coefficient A2 vanishes, is close to that of the corresponding high molecular mass polymer solution without cross-links so that solvent quality may be defined in the same way as the corresponding precursor polymer solution. We quantified the swelling and deswelling of PVAc gels relative to their size at the theta temperature, and also determined the effect of T on the shear modulus of these gels. It was found that both swelling and deswelling data could be reduced to a universal scaling equation of the same general form as derived from renormalization group (RG) theory for flexible linear polymer chains in solutions.Graphical abstractVariaton of the volumetric swelling factor as a function of the reduced temperature for PVAc gels swollen in isopropyl alcohol.

Assessing heterogeneous groundwater systems: Geostatistical interpretation of well logging data for estimating essential hydrogeological parameters

This research presents an unsupervised learning approach for interpreting well-log data to characterize the hydrostratigraphical units within the Quaternary aquifer system in Debrecen area, Eastern Hungary. The study applied factor analysis (FA) to extract factor logs from spontaneous potential (SP), natural gamma ray (NGR), and resistivity (RS) logs and correlate it to the petrophysical and hydrogeological parameters of shale volume and hydraulic conductivity. This research indicated a significant exponential relationship between the shale volume and the scaled first factor derived through factor analysis. As a result, a universal FA-based equation for shale volume estimation is derived that shows a close agreement with the deterministic shale volume estimation. Furthermore, the first scaled factor is correlated to the decimal logarithm of hydraulic conductivity estimated with the Csókás method. Csókás method is modified from the Kozeny-Carman equation that continuously estimates the hydraulic conductivity. FA and Csókás method-based estimations showed high similarity with a correlation coefficient of 0.84. The use of factor analysis provided a new strategy for geophysical well-logs interpretation that bridges the gap between traditional and data-driven machine learning techniques. This approach is beneficial in characterizing heterogeneous aquifer systems for successful groundwater resource development.

New insights into ion migration time under nonuniform electric fields: Mechanism and application to designing fast exhaustive electroextraction

Electrokinetic techniques, such as electrophoresis, electroextraction, and electrodialysis, have found a wide range of applications in fields such as chemical engineering, chemistry, biology, and environmental science. A critical parameter in these techniques is the time required for ion migration, which is often driven by a nonuniform three-dimensional electric field. However, the influence of the inhomogeneity of an electric field on ion migration time remains unclear, impeding procedures for its control. Herein, for the first time, we propose a concise, universal equation that clearly describes the features of electrophoresis times in nonuniform electric fields and reveals a linear relationship between ion migration time and the degree of dispersion of the electric field (or ion velocity). This discovery should facilitate the rational design for development of electrokinetic techniques to replace previous trial-and-error approaches. We demonstrate the viability of our method using a test case involving the design of an electroextraction device with high efficiency and matrix tolerance. The device with the optimized electric field geometry enables the exhaustive enrichment of crystal violet from a milliliter-level donor phase into a microliter-level acceptor phase within 540 s and avoids agitation. The direct, rapid electroextraction of trace analytes from complex essential oils and honey samples within 300–480 s is realized using this device, which is further coupled with liquid chromatography-mass spectrometry. The resulting analytical method displays low limits of detection (0.01–0.06 ng·mL−1; 0.08–0.30 μg·kg−1), overcoming the issues of time- and labor-intensive and error-prone sample preparation.

Rational Design of Reliable Computational Protocols for Predicting Dielectric Constants of Gaseous Molecules.

A rapid prediction of the dielectric constants from a wide range of organic compounds is of paramount importance given the pressing need to find alternatives to SF6, one of the seven greenhouse gases. However, the availability of a universally applicable equation for predicting dielectric constants remains limited. This study endeavors to systematically develop a universal equation for predicting the dielectric constants of gaseous organic molecules in a systematic manner. The reliability of these newly developed equational protocols is evaluated through both quantitative (i.e., root-mean-squared deviation) and qualitative (i.e., Spearman's rank correlation coefficient) analyses. Equational optimization of the traditionally unreliable Clausius-Mossotti equation highlights the critical role of selecting a suitable variable to be incorporated into an adapted Clausius-Mossotti equation, ultimately enhancing the predictive accuracy. Furthermore, it is revealed that the nature of the chosen variable has a more significant impact on prediction accuracy than the quantity of variables introduced. These findings shed light on the ongoing efforts of developing a dependable protocol for predicting not only dielectric constants but also other vital insulating properties, such as dielectric strength.

Time of concentration estimated of overland flow

Time of concentration (Tc) is a crucial aspect in the hydrological model, especially for determining flood discharge. Time concentration is the amount of time required for water to go from a watershed’s farthest point to its outflow. Although it is an important value, however, Tc does not have a universal equation that can be used as a reference. Based on the literature review, there are several concentration time calculation methods. Each method has its parameters and approach to produce varied values. Several experimental methods were applied to calculate concentration time at sites, among others are Kirpich, SCS Lag, and FAA. The calculation results are displayed in a dendrogram with group division by using the Euclidean approach. The calculation results show that the difference in Tc values can reach up to 500%, hence Grimaldi calls it a paradox in modern hydrology.

Artificial Neural Network for Forecasting Reference Evapotranspiration in Semi-Arid Bioclimatic Regions

A correct determination of irrigation water requirements necessitates an adequate estimation of reference evapotranspiration (ETo). In this study, monthly ETo is estimated using artificial neural network (ANN) models. Eleven combinations of long-term average monthly climatic data of air temperature (min and max), wind speed (WS), relative humidity (RH), and solar radiation (SR) recorded at nine different weather stations in Tunisia are used as inputs to the ANN models to calculate ETo given by the FAO-56 PM (Penman–Monteith) equation. This research study proposes to: (i) compare the FAO-24 BC, Riou, and Turc equations with the universal PM equation for estimating ETo; (ii) compare the PM method with the ANN technique; (iii) determine the meteorological parameters with the greatest impact on ETo prediction; and (iv) determine how accurate the ANN technique is in estimating ETo using data from nearby weather stations and compare it to the PM method. Four statistical criteria were used to evaluate the model’s predictive quality: the determination coefficient (R2), the index of agreement (d), the root mean square error (RMSE), and the mean absolute error (MAE). It is quite evident that the Blaney–Criddle, Riou, and Turc equations underestimate or overestimate the ETo values when compared to the PM method. Values of ETo underestimation ranged from 1.9% to 66.1%, while values of overestimation varied from 0.9% to 25.0%. The comparisons revealed that the ANN technique could be adeptly utilized to model ETo using the available meteorological data. Generally, the ANN technique performs better on the estimates of ETo than the conventional equations studied. Among the meteorological parameters considered, maximum temperature was identified as the most significant climatic parameter in ETo modeling, reaching values of R and d of 0.936 and 0.983, respectively. The research showed that trained ANNs could be used to yield ETo estimates using new data from nearby stations not included in the training process, reaching high average values of R and d values of 0.992 and 0.997, respectively. Very low values of MAE (0.233 mm day−1) and RMSE (0.326 mm day−1) were also obtained.

Predicting Covid-19 pandemic waves with biologically and behaviorally informed universal differential equations

During the COVID-19 pandemic, it became clear that pandemic waves and population responses were locked in a mutual feedback loop in a classic example of a coupled behavior-disease system. We demonstrate for the first time that universal differential equation (UDE) models are able to extract this interplay from data. We develop a UDE model for COVID-19 and test its ability to make predictions of second pandemic waves. We find that UDEs are capable of learning coupled behavior-disease dynamics and predicting second waves in a variety of populations, provided they are supplied with learning biases describing simple assumptions about disease transmission and population response. Though not yet suitable for deployment as a policy-guiding tool, our results demonstrate potential benefits, drawbacks, and useful techniques when applying universal differential equations to coupled systems.

Robust reconciliated KD from end-point flow cytometry and time-resolved kinetic experiments on live cells, using a universal non-pseudo first-order binding equation

Robust reconciliated KD from end-point flow cytometry and time-resolved kinetic experiments on live cells, using a universal non-pseudo first-order binding equation

Universal Equations for Higher Genus Gromov–Witten Invariants from Hodge Integrals

Universal Equations for Higher Genus Gromov–Witten Invariants from Hodge Integrals