Universal Equation Research Articles

Systematics of Crystalline Oxide and Framework Compression

A universal equation of state of solids is one of the far goals of condensed matter science. Here, it is shown that within pressures of 2–100 GPa, the compression of oxides and oxide-based networks follows a linear relation between the molar volume and the combined ionic volume that is based on the pressure-dependent crystal radii at any pressure. This relation holds for simple and complex oxides and modified networks such as alumosilicates, beryllosilicates, borates, and empty zeolites. Available compression data for halides and metal-organic frameworks are also consistent with this relation. Thus, the observed relation also serves as a measure for pore-space filling in cage structures.

Strong impact and engraving characteristics of multi-layer metallic materials under a two-stage combustion condition

Abstract This work is focused on the strong deformation motion mechanism of multi-layer metallic materials under extreme pressure conditions accompanied by a strong impact effect between the projectile composed of multi-layer metallic materials and the steel barrel of the launcher itself. Here, this transient engraving process of the projectile with complicated stress–strain based on a new type of structure and propulsion pattern is firstly studied by proposing a new physical and mathematical model with a coupling of dynamical equations and two-stage combustion ballistic equations. Comparisons of engraving distance of computational results are done with experimental studies, and a reasonable match has been obtained in these comparisons. Further, the thickness effect of the metal jacket of the projectile on the engraving stress and deformation level is analyzed to obtain universal engraving resistance equations. The results have also shown that the projectile's whole transient deformation motion process in the launcher can be divided into three periods due to the initial slide impact effect under the first-stage propellant gas and the later propelling effect as the second-stage propellant is ignited. However, the engraving durations are all less than 0.7 ms with different levels of elastic-plastic deformations between multi-layer metallic materials for different conditions.

Train-induced aerodynamic characteristics of vertical sound barriers influenced by several factors

Investigations into the aerodynamic properties of vertical sound barriers exposed to high-speed operations employ computational fluid dynamics. The primary focus of this research is to evaluate the influence of train speed and the distance (D) from the track centerline under various operating conditions. The findings elucidate a marked elevation in the aerodynamic effect amplitude on sound barriers as train speeds increase. In single-train passages, the aerodynamic effect amplitude manifests a direct relationship with the square of the train speed. When two trains pass each other, the aerodynamic amplitude intensifies due to an additional aerodynamic increment on the sound barrier. This increment exhibits an approximate quadratic correlation with the retrograde train speed. Notably, the impact of high-speed trains on sound barrier aerodynamics surpasses that of low-speed trains, and this discrepancy amplifies with larger speed differentials between trains. Moreover, the train-induced aerodynamic effect diminishes significantly with greater distance (D), with occurrences of pressure coefficient (CP) exceeding the standard thresholds during dual-train passages. This study culminates in the formulation of universal equations for quantifying the influence of train speed and distance (D) on sound barrier aerodynamic characteristics across various operational scenarios.

Numerical calculation the fracture toughness of square section beam under three-point bending test

A universal equation is proposed to determine specific fracture energy based on numerical calculations by finite element methods in the ANSYS system referring to the three-point bending of a square beam arranged edgewise on supports. Numerical dependences of the specimen compliance on the crack length were represented as the 5th and 6th degree polynomials on the relative value of Δl/h, where Δl is the crack length and h is the half length of the square diagonal. To calculate the specific fracture energy, we used the derivative of specimen compliance by the crack length. The analysis has shown that finite value of specific fracture energy at Δl→0 is obtained when the decomposition term at Δl/h is equal to 0. A satisfactory agreement between the specific fracture energy values for the 5th and 6th degree decompositions is observed only at Δl/h ≈ 1. As the values of Δl decrease, the difference becomes increasingly significant. The averaging of coefficients at corresponding Δl/h degrees of two considered decompositions allows us to find a power function that weakly depends on the Δl/h ratio and leads to a consistent dependence of the specific fracture energy on the crack length. Due to the performed calculations, a universal equation is obtained to determine the specific fracture energy according to the test data of square beams by three-point bending in a wide range of geometric dimensions.

Experimental and numerical study on flow dynamics and universal characteristics of ventilated supercavities behind different cavitators

In this study, physical aspects of a ventilated supercavity behind different cavitator geometries such as the hydrodynamic characteristics, distribution of pressure within the cavity, hysteresis phenomenon, and gas leakage mechanism were qualitatively and quantitatively investigated using experimental and numerical methods. For the simulation and tunnel tests, we employed five cavitators, each with different angles (45°, 60°, 90°, 135°, and a 180° cavitator, commonly referred to as a disk cavitator), all sharing the same diameter. The results revealed that the drag force experienced on the cavitator decreased linearly with an increase in the ventilation rate, and a consistent trend was observed for all test cavitator angles. Through experimental measurements, a universal equation has been derived to predict the drag force exerted on a supercavitating vehicle employing a cavitator. In addition, the pressure distribution inside the supercavity was significantly influenced by the angle of the cavitator. The pressure kept almost unchanged in the first half of supercavity; a slight increase in pressure occurred in the remainder of the supercavity. Twin-vortex gas leakage mode was clearly observed. The distance between the two hollow vortices increased significantly, whereas the incline angle of these vortices and the horizontal line changed insignificantly.

Equações universais para as distribuições de chuva dos métodos SCS e Huff

ABSTRACT The temporal distribution of design rainfall hyetographs can be obtained through various procedures. One such method involves using temporal distribution curves to disaggregate a rainfall value of longer duration into chronological values within shorter time intervals. This is demonstrated by SCS distribution curves for durations of 6 and 24 hours and the well-known Huff curves. Another approach involves deriving temporal distribution using design hyetograph calculation methods, such as the Chicago and alternating block methods, based on Intensity-Duration-Frequency (IDF) equations. This paper aims to combine these approaches and develop universal equations capable of accurately fitting smooth rainfall time distribution curves. The advantage is the replacement of tables, like SCS and Huff, with analytical equations, enhancing usability in spreadsheets. Furthermore, these universal equations can determine the temporal rainfall distribution using an IDF equation or fitting a specified design hyetograph like Euler type II. Four numerical examples are provided.

Cosmological constraints on 4-dimensional Einstein-Gauss-Bonnet gravity

4-Dimensional Einstein-Gauss-Bonnet (4DEGB) gravity has garnered significant attention in the last few years as a phenomenological competitor to general relativity. We consider the theoretical and observational implications of this theory in both the early and late universe, (re-)deriving background and perturbation equations and constraining its characteristic parameters with data from cosmological probes. Our investigation surpasses the scope of previous studies by incorporating non-flat spatial sections. We explore consequences of 4DEGB on the sound and particle horizons in the very early universe, and demonstrate that 4DEGB can provide an independent solution to the horizon problem for some values of its characteristic parameter α. Finally, we constrain an unexplored regime of this theory in the limit of small coupling α (empirically supported in the post-Big Bang Nucleosynthesis era by prior constraints). This version of 4DEGB includes a geometric term that resembles dark radiation at the background level, but whose influence on the perturbed equations is qualitatively distinct from that of standard forms of dark radiation. In this limit, only one beyond-ΛCDM degree of freedom persists, which we denote as α̃ C . Our analysis yields the estimate α̃ C = (-9 ± 6) × 10-6 thereby providing a new constraint of a previously untested sector of 4DEGB.

РАСЧЁТ НА ПРОЧНОСТЬ И ПРОВЕРКА ЖЁСТКОСТИ СТАТИЧЕСКИ ОПРЕДЕЛИМОЙ БАЛКИ ДВУТАВРОВОГО СЕЧЕНИЯ

This paper presents a strength calculation for a statically determinate I-beam. Diagrams of internal force factors (transverse forces and bending moments) are constructed and the number of the I-beam is selected according to the given external load and the values of the material strength characteristics. The given material characteristics are permissible normal stress, elastic modulus and permissible shear stress. The strength of a beam with a selected cross-section for shear stresses was tested. To construct the I-beam elastic line, the deflections of cross-sections with a unit interval along the length are calculated. The beam deflections were calculated using the universal elastic line equation. The obtained value of the maximum beam deflection made it possible to draw a conclusion about the beam sufficient hardness and operability under given external loads.

Domain wall creep motion dynamics in CoFeB nanowire strips of different thicknesses using micromagnetic simulation approach

Field-induced domain wall motion on thin magnetic films with perpendicular anisotropy has long been attributed with the universal creep theory, in which the domain wall (DW) is able to experience a slow-moving motion with driving fields below the depinning threshold. Despite the numerous research that has been conducted in regards to this phenomenon, creep motion thus far has yet to be observed on a typical single-layered magnetic film. The effects of the film’s thickness towards the creep motion are also scarcely explored. In this study, we conduct micromagnetic simulations of CoFeB nanowire strips with perpendicular anisotropy and varying thicknesses to investigate the dynamics of the creep motion being exhibited. We then analyze the obtained DW velocities and its’ agreement with the universal creep law equation. The velocities obtained with low driving fields is found to be in an agreement with the creep law equation. The varying thicknesses also seem to affect the overall DW velocity and DW width.

ПОСТРОЕНИЕ УПРУГОЙ ЛИНИИ БАЛКИ И ОПРЕДЕЛЕНИЕ ВЕЛИЧИНЫ И НАПРАВЛЕНИЯ ГЛАВНЫХ НАПРЯЖЕНИЙ В СЕЧЕНИИ БАЛКИ

The paper uses the data from diagrams of I-beam transverse forces and bending moments to calculate the values and directions of primary stresses at three points of the beam cross-section – on the neutral axis, above and below it. To calculate the values of primary stresses, the graphic analytical method with the construction of Mohr's circles is used. Further, the article presents an algorithm for constructing a beam deflection line and calculating cross-section deflections. To determine deflections, the universal beam deflection line equation is used. After determining the largest deflection value, conclusion is made that the hardness condition of a steel I-beam is met.

Оценка начального развития лесопарковых зон, создаваемых на урбанизированных территориях

The article is devoted to the development of methods for assessing the state of initial development of forest park zones created in suburban areas. The purpose of the research is to consider the possibility of introducing a multiplicative indicator that equally takes into account these indicators, to study its extreme characteristics for homogeneous and heterogeneous land plots. The relationship between factor C from the universal equation of soil losses and the weight of dry biomass of deciduous trees which, in turn, are regression dependent on NDVI (Normalized difference vegetation index), a numerical indicator of the quality and quantity of woody vegetation on the site, is considered. Two criteria are proposed to assess the initial state of development of the urban forest park zone. It is shown that the first criterion has a minimum at a certain NDVI value. The second criterion is presented in the form of a functional containing the function of the relationship between NDVI and factor C. It is determined that the extreme of this functional has the form of a function of the inverse relationship between NDVI and factor C. The real existence of such an inverse relationship between NDVI and C opens up new opportunities for using this function in metrology.

Brain Tissue Oxygen Dynamics Under Localised Hypoxia in the Awake State and the Physical Neuroprotective Effects of General Anaesthesia.

Brain health directly depends on maintaining a level of tissue oxygen that is high enough to avoid global hypoxia and local brain ischaemia. It is well documented that general anaesthesia has an anti-hypoxic neuroprotective effect. Previous studies of this effect primarily assessed the biochemical actions of anaesthetics. Physical actions were not well studied because the quantification of oxygen dynamics has only recently been described. Based on known oxygen, blood, and neuronal measurements, under various anaesthesia protocols and in the awake state, we mathematically analysed physical anaesthesia effects on oxygen distribution for localised hypoxia. From this, we built a universal equation of oxygen dynamics which can be applied to both animal and human subjects in awake and anaesthetised states, under normoxia, hyperoxia, and hypoxia. Using this equation, we determined that a proper anaesthesia protocol can protect up to 167 mm3 of local hypoxic cortical brain tissue via oxygen diffusion from healthy neighbouring areas.

Comparative Study of Aflatoxin M1 Carry-Over from Feed to Raw ‎Milk in Cow, Buffalo, Sheep, and Goats in Different Areas of ‎Baghdad Province

Mycotoxin aflatoxin B1 (AFB1) is a threat to food safety and human health because it is present in animal feed and is metabolized into aflatoxin M1 (AFM1), a more toxic form, during lactation. The aim of this study was to quantify AFM1 concentrations in raw milk of buffalos, cows, sheep, and goats sampled randomly from four regions within Baghdad ‎Province, Iraq, and to compare these levels with the maximum allowable levels set forth by the ‎European Commission (EC), the Iraqi Standard Specification (IQS), and the food and Drug Administration (FDA). The carry-over of AFB1 from feed to AFM1 in milk were also calculated for each of the ‎studied species. A total of 200 random samples, including 50 each from cows, buffaloes, ‎sheep, and goats, were collected from farms located in Zu'afraniya, Nahrawan, Abu Ghraib, and ‎Fedhalia regions. AFM1 and AFB1 concentrations were determined using the ‎enzyme-linked immunosorbent assay (ELISA). Raw milk samples from cows, sheep, buffaloes, and goats were all found to have AFM1 concentrations that were below the limits set by the EC, IQS, and FDA. Animal feed samples, on the other hand, had AFB1 concentrations of 10.08, 5.95, 4.27, and 7.10 ppb for ‎buffaloes, cows, sheep, and goats, respectively. The observed carry-over rates ranged from 0.36% ‎in goats to 0.78% in buffaloes to 0.66% in cows. Multiple factors, including animal species, ‎are considered, and it is determined that a universal carry-over equation cannot be applied to all cases. ‎Therefore, it is essential to regularly monitor AFM1 levels in milk from various animal species in order to ‎lessen potential health risks. Furthermore, the study suggests enhancing agricultural and veterinary ‎practices to better regulate feed quality for dairy animals‎‎‎‎.

On the solutions of universal differential equation

The objective of this work is to give expressions for solutions of universal differential equation and finally, as application, provides the unique grouplike solution, by dévissage, of Knizhnik-Zamolodchikov equation satisfying asymptotic conditions, i.e. solution of KZn can be obtained using solution of KZ n−1 and the noncommutative generating series of hyperlogarithms. These expressions are obtained using the algebraic combinatorics on noncommutative formal series with holomorphic coefficients and a Picard-Vessiot theory of noncommutative differential equations.

Clarification of the Regional Methodology for Calculating Potential Soil Flushing from Meltwater for the Northern Forest-Steppe of Central Siberia

Abstract—The need to verify, modernize and refine existing models for calculating potential soil flushing from the effects of meltwater is due to the small number of studies of this type of erosion in the forest-steppe zone of Central Siberia and, as a consequence, the inability to reliably determine how accurate the calculation methods are in their current form under these conditions. For the agricultural zone of the Krasnoyarsk Territory, a regional model has been developed for calculating potential soil flushing based on a Universal equation and the Instructions’ formula. This paper presents the results of its verification, performed using the results of the author’s field measurements of soil flushing from meltwater by measuring removal cones on agricultural lands of the northern forest-steppe of Central Siberia (Krasnoyarsk forest-steppe). A refined version of the Regional Methodology is proposed, adapted to local hydrometeorological conditions and representing the formula of this model with an added correction factor \(K,\) taking into account the influence of the previous autumn moistening of soils and the intensity of water flow to the soil surface during snowmelt. Refinement and adaptation of the methodology allowed to increase the accuracy of the results of its application by an average of three times compared to the original type of the model, the average error decreased from 0.3 to 0.11. The refined version of the Regional methodology was tested in the course of the author’s research of snow-fall soil erosion in the Krasnoyarsk forest-steppe.

Effect of CsBr on the optical properties and electrical conductivity of PVP/PVA composite for flexible optoelectronic devices

This research contributes to the field by investigating the novel combination of PVP/PVA with CsBr NPs and elucidating the structural, optical, and electrical modifications that result from this combination, particularly focusing on the potential for energy storage and semiconductor characteristics of CsBr NPs. The insertion of CsBr NPs as a nanofiller has increased the degree of amorphousness in the PVP/PVA mixture, according to the XRD of the samples under investigation. The degree of crystallinity reduced from 32.15 to 18.56. FT-IR confirms the interaction or complexation of CsBr NPs with polymer blend. AFM investigations have revealed modifications in the surface morphology of the prepared films from smooth to rough as a result of the CsBr nanofiller. Utilizing UV/vis absorption spectra, the values of direct and indirect band gaps were determined. The optical band gaps decreased as CsBr NPs concentration increased, reaching a maximum of 3.65 eV for permitted indirect transition. By Jonscher's universal power equation, composites have a higher AC conductivity at high frequencies. It is also found to rise with increasing nanoparticle concentration. The film containing 15 wt% CsBr NP exhibits good optical properties, good conductivity, and a high dielectric constant. Dielectric constants (ε′ and ε′′) improved with increasing CsBr NPs concentration and decreased with rising frequency. The polymer nanocomposite acquired met the essential optical and electrical criteria, indicating its suitability for various electronic applications. These applications encompass functions such as energy storage devices, gas sensors, and optoelectronic devices.

Estimating omnidirectional urban vertical wind speed with direction-dependent building morphologies

A main external factor that limits the energy assessment of high-rise buildings in urban areas is the vertical wind conditions. Conventional buildings' energy assessment tools apply a universal vertical wind profile estimation equation in all directions and only consider four typical terrain types. However, the various shape and configurations of buildings in cities can induce the unique wind speed in each direction, and the vertical wind speeds in the same terrain type can be different even in the same city. To get more realistic vertical wind conditions, this study developed an omnidirectional urban vertical wind speed estimation method with direction-dependent building morphologies. A pie-shaped segment method is applied to calculate building morphological features in approaching wind direction. Machine learning methods are developed to calculate parameters of the modified direction-dependent power law urban wind function to convert the Typical Meteorological Year (TMY) wind speed to urban vertical wind speeds. To validate the proposed method, wind tunnel data in Hong Kong are collected for a case study. The results indicate that the proposed method with morphological inputs can effectively estimate the vertical wind speed at different wind directions and heights, and deep neural networks and support vector regression have better performance.

Construction of universal equations for knot attributes of three coniferous species.

We constructed base model, dummy variable model, and mixture model with three variables including knot diameter, loose knot length, and sound knot length with three typical coniferous species, Pinus koraiensis, Larix olgensis, and Pinus sylvestris var. mongolica, from the Linkou Forestry Bureau and Mengjiagang forest farm in Heilongjiang Province in 2020. We analyzed the differences in knot properties among different tree species and simplified the modeling work. Firstly, we collected relevant knot property data through the sectioning method based on relevant literature, transformation of the model form and substitution of related variables to conduct a base model. We transformed the species into dummy variables as qualitative factors, and introduced the dummy variable model of the relevant attributes into the base model. We introduced the random effects of sample trees and sample plots when constructing the mixture model. By comparing evaluation indicators, such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), the mixture model with the best fitting effect was selected. We selected the optimal universal equation by comparing the fitting accuracy of the base model, dummy variable model and mixture model. The fitting accuracy of the dummy variable model and mixture model was higher than that of the basic model. The evaluation indicators (AIC and BIC) showed that the mixture model had a better fitting effect on knot properties than the dummy variable model. In the model comparison results, R2 of mixture models for sound knot length, the loose knot length, and knot diameter increased by 13.2%, 84.8% and 40.3%, respectively. The predictive accuracy of the three base models for different tree species' knot attributes was above 90%, and both the prediction accuracy of the dummy variable model and mixture model were above 94%, indicating that the constructed models could well predict knot-related properties. From the perspective of tree species, the sound knot length, knot diameter, and loose knot length was in order of P. sylvestris var. mongolica > P. koraiensis > L. olgensis. Fitted results of the dummy variable model and the mixture model were superior to the basic model, with higher accuracy.

ZAFG Method for Quantitative Characterization of Spherical Particles: Deriving a Universal Equation for Geometrical Correction.

This study introduces a universal equation to calculate the geometrical correction factor (G) as the fourth factor in the conventional ZAF method for quantifying spherical particles (specifically, NIST-K411 glass microspheres mounted on bulk carbon substrate). Note that the fluorescence correction factor (F) is not considered in this study. Our findings demonstrate that the G factor, as a function of the particle diameter (D) and the range of emitted X-rays in a bulk sample (Xe), provides the best model. Xe depends on the chemical composition and accelerating voltage. We observed excellent agreement between the G factor predicted by our model and experimental data obtained from NIST-K411 standard particles. Our results show that when Xe is greater than D, the G factor decays exponentially, independent of the incident electron energy, X-ray lines, and chemical composition of the particles. We also found that when DXe > 1, the particle behaves as a bulk sample, and G = 1. Notably, our data indicate that the G factor depends only on DXe, not on the chemical composition or beam energy.

A Universal Equation to Predict Ωm from Halo and Galaxy Catalogs

We discover analytic equations that can infer the value of Ωm from the positions and velocity moduli of halo and galaxy catalogs. The equations are derived by combining a tailored graph neural network (GNN) architecture with symbolic regression. We first train the GNN on dark matter halos from Gadget N-body simulations to perform field-level likelihood-free inference, and show that our model can infer Ωm with ∼6% accuracy from halo catalogs of thousands of N-body simulations run with six different codes: Abacus, CUBEP3M, Gadget, Enzo, PKDGrav3, and Ramses. By applying symbolic regression to the different parts comprising the GNN, we derive equations that can predict Ωm from halo catalogs of simulations run with all of the above codes with accuracies similar to those of the GNN. We show that, by tuning a single free parameter, our equations can also infer the value of Ωm from galaxy catalogs of thousands of state-of-the-art hydrodynamic simulations of the CAMELS project, each with a different astrophysics model, run with five distinct codes that employ different subgrid physics: IllustrisTNG, SIMBA, Astrid, Magneticum, SWIFT-EAGLE. Furthermore, the equations also perform well when tested on galaxy catalogs from simulations covering a vast region in parameter space that samples variations in 5 cosmological and 23 astrophysical parameters. We speculate that the equations may reflect the existence of a fundamental physics relation between the phase-space distribution of generic tracers and Ωm, one that is not affected by galaxy formation physics down to scales as small as 10 h −1 kpc.