Simple Formula Research Articles

Free energy formulae for confined nematic liquid crystals based on analogies with Kirchhoff–Routh theory in vortex dynamics

Active nematics are influenced by alignment angle singularities called topological defects. The localization of these defects is of major interest for biological applications. The total distortion of alignment angles due to defects is evaluated using Frank free energy, which is one of the criteria used to determine the location and stability of these defects. Previous work used the line integrals of a complex potential associated with the alignments for the energy calculation (Miyazako and Nara 2022 R. Soc. Open Sci . 9 , 211663 (doi: 10.1098/rsos.211663 )), which has a high computational cost. We propose analytical formulae for the free energy in the presence of multiple topological defects in confined geometries. The formulae derived here are an analogue of Kirchhoff–Routh functions in vortex dynamics. The proposed formulae are explicit with respect to the defect locations and conformal maps, which enable the explicit calculation of the energy extrema. The formulae are applied to calculate the locations of defects in so-called doublets and triplets by solving simple polynomial formulae. A stability analysis is also conducted to detect whether defect pairs with charges ± 1 / 2 are stable or unstable in triplet regions. Our numerical results are shown to match the experimental results (Ienaga et al. 2023 Soft Matter 19 , 5016–5028. (doi: 10.1039/d3sm00071k )).

Lattice points on polyominoes of inversion sequences

Inversion sequences of length n are positive integer sequences e 1 e 2 …e n such that 1 ≤ ei ≤ i for all 1 ≤ i ≤ n. These sequences are in bijection with the permutations of [n]. This paper focuses on the polyomino or barpgraph representation of the inversion sequences. More precisely, we study the distribution of lattice points on these polyominoes. We find the generating functions respect to the length, the number of interior vertices, corners, and vertices of a given degree. We also give simple explicit formulas for the total values of these parameters over all polyominoes of inversion sequences of length n. Throughout this work, we use symbolic computer algebra to facilitate the computations.

Axial and eccentric compressive behavior of partially encased channel–concrete composite columns with bolted connections in modular buildings

This paper introduces a novel partially encased channel–concrete composite (PECC) column for modular buildings, aiming to eliminate the need for cast-in-place concrete and facilitate rapid assembly. The PECC column consists of two prefabricated modules connected by high-strength bolts. To evaluate the column's viability, six slender specimens—one bare steel column and five composite columns—were tested under axial and eccentric compression. Variables considered included the presence of concrete, the type of transverse connections, bolt spacing, and load eccentricity ratio. The compression performance of the PECC columns was analyzed by examining their failure patterns, load–deformation responses, initial stiffness, compressive capacity, and ductility. Test results revealed that the PECC columns failed due to global buckling, concrete spalling, and crushing. The bolted connections effectively prevented module separation, enabling the PECC columns to exhibit favorable compressive behavior. The reinforced concrete encased in the channel delayed the column's buckling failure, increasing its initial stiffness and compressive capacity by 98% and 198%, respectively. Using perforated steel plates instead of transverse links between the concrete and the channel enhanced the column's initial stiffness by 20% but had little effect on its compressive capacity. Reducing the bolt spacing improved the column's initial stiffness and compression resistance by 50% and 5%, respectively. Additionally, a finite element model for the PECC columns was developed and validated against test results. Finally, simplified formulas derived from Eurocode 4 were proposed to estimate the resistance of PECC columns under axial and eccentric compression.

Pengaruh Usaha Budidaya Bebek Petelur Terhadap Perekonomian Keluarga di Desa Sukamerindu Kecamatan Pemulutan Barat

This research aims to find out the influence of petal duck business on the family economy in Sukamerindu Village, Indralaya district of Ogan Ilir. The approach used in this research is quantitative with the type of descriptive research. The population of this research is an entrepreneurial duck with a sample of 30 entrepreneurs using a census sample technique. Data collection techniques using observation and lifting. Data analysis techniques using simple linear regression formulas. The results of the research showed that there was an influence between the business of the duck on the family's economy. For influence business ducks belong to the low category. With the result of a ritung value > rtable that is a positive influence on the economy of the family that has a contribution of 0.153 or. That means every 1% increase in the rate of breeding of the duck (X), then the increase in income (Y) will increase by 0.153. As far as the positive impact of the breeding of the duck is concerned, it can be seen from the result that the majority of the community that has an undertaking of breeding ducks is able to meet the daily needs of quality food, have sufficient water, and are able to satisfy daily needs. It can be concluded that the results of the research there is a positive relationship between the cultivation of ducks petal against the economy of the family in the village of Sukamerindu district of Ogan Ilir.

Разработка комплексного показателя оценки состояния городского электротранспорта для органов исполнительной власти Российской Федерации

This article analyzes 115 cities on the territory of the Russian Federation in which one or more urban electric transport systems operate. It is determined that in the modern industry there is no single comprehensive indicator of the state of urban electric transport, which would allow an assessment of the state of systems not only in relation to their own indicators of previous years, but also in relation to other, similar systems. A comprehensive indicator is proposed that will allow a comprehensive assessment of the state of urban electric transport and interpret it in numerical terms for its application by state and regional authorities, allowing to quickly draw conclusions and make a decision on further adjustment of the functioning of the electric transport system, characterized by a relatively simple formula for calculation and does not require specific competencies for those conducting the analysis. The key indicators of urban electric transport are systematized, including those related to the operated energy infrastructure, linear infrastructure, park facilities, including technical buildings and structures for system maintenance, indicators related to rolling stock and its key technical characteristics, as well as the availability of urban electric transport for residents of the considered locality and passenger flows within this framework systems. The boundaries of the values of the final indicator have been determined, within which the state of urban electric transport will be assessed by state and regional authorities as satisfactory or unsatisfactory and requiring decisions on revising approaches to the development of the system within the framework of strategic transport planning documents.

From higher-spin gauge interactions to Compton amplitudes for root-Kerr

We develop massive higher-spin theory as a framework for describing dynamics of rotating compact objects, such as Kerr black holes. In this paper, we explore gauge interactions up to quartic order and corresponding Compton amplitudes of higher-spin massive objects coupled to electromagnetism and Yang-Mills theory. Their classical counterparts are known as root-Kerr gauge-theory solutions, whose amplitudes are closely related to those of Kerr black holes. We use three distinct approaches: (i) massive higher-spin gauge symmetry to introduce cubic interactions for all spins and the quartic interactions up to spin 3, which is implemented both off shell and via Ward identities; (ii) a chiral higher-spin approach to construct quartic Lagrangians with correct degrees of freedom to all spins; (iii) on-shell functional patterns before and after taking the classical limit to constrain the Compton amplitudes. As final results, we arrive at simple local formulae for the candidate root-Kerr Compton amplitudes both in the quantum regime and classical limit, to all orders in spin. This is a precursor to the gravitational Kerr case, which is presented in a follow-up paper.

Cosmological correlators with double massive exchanges: bootstrap equation and phenomenology

Using the recently developed cosmological bootstrap method, we compute the exact analytical solution for the seed integral appearing in cosmological correlators with double massive scalar exchanges. The result is explicit, valid in any kinematic configuration, and free from spurious divergences. It is applicable to any number of fields’ species with any masses. With an appropriate choice of variables, the results contain only single-layer summations. We also propose simple approximate formulas valid in different limits, enabling direct and instantaneous evaluation. Supported by exact numerical results using CosmoFlow, we explore the phenomenology of double massive exchange diagrams. Contrary to single-exchange diagrams with ubiquitous Lorentz-covariant interactions, the size of the cubic coupling constant can be large while respecting perturbativity bounds. Because of this property, the primordial bispectrum from double-exchange diagrams can be as large as, coincidentally, current observational constraints. In addition to being sizable on equilateral configurations, we show that the primordial bispectrum exhibits a large cosmological collider signal in the squeezed limit, making the double massive exchanges interesting channels for the detection of massive primordial fields. We propose to decisively disentangle double-exchange channels from single-exchange ones with cosmological observations by exploiting the phase information of the cosmological collider signal, the inflationary flavor oscillations from multiple fields’ species exchanges and the double soft limit in the primordial trispectrum.

Hydrogen isotopic ratio by residual gas analysis during the JET DT campaigns

Abstract The analysis of hydrogen isotope content is crucial for understanding the operation of fusion devices. Hydrogen isotopic analysis in the core and plasma edge is conducted through neutron and spectroscopic diagnostics. In the case of exhaust gas, mass spectrometry is employed using residual gas analyzers (RGAs), along with optical gas analysis (OGA) utilizing an optical Penning gauge. The use of traditional quadrupole mass spectrometers for RGA encounters challenges during discharges with tritium gas due to signal overlap of different hydrogen molecules at the same mass number. This paper introduces a novel technique to address this issue through a cross-related analysis of RGA data with OGA results. Another consideration in mass spectrometry analysis is the instrument’s varying sensitivity concerning the gas mass number. The paper includes gas calibration data results for all the quadrupoles used in the JET gas analysis. Hydrogen isotopic ratios are calculated from RGA detected currents using simple formulas. The results of this procedure are presented for selected DT JET discharges in relation to the JET pulse time, and they are compared with corresponding optical data. Time-averaged hydrogen isotopic ratio values are computed for numerous discharges during the DT and T campaigns.

Using Rejection Sampling Probability of Acceptance as a Measure of Independence

This article proposes a new association statistic for determining whether random variables are statistically independent. The proposed association statistic can also be used to examine the strength of both linear and nonlinear dependency between variables. This statistic is derived by examining how the conditional probabilities of events differ from their corresponding marginal probabilities. The new statistic is defined in terms of the probability of acceptance commonly associated with the Accept–Reject algorithm and has a very simple formula. The simulated density of the probability of acceptance can be used to measure the degree of uncertainty of the estimated values of the new association statistic. The results from simulations as well as examples that employ real data indicate that this new association statistic is very powerful in detecting linear and nonlinear associations between two random variables. Supplementary materials for this article are available online.

Determination of the required degree of surface perforation of collecting drainage pipelines

The operational characteristics of a collecting pressure pipeline, where the flow enters through holes and slots along its length in a turbulent mode, and a pressure drainage pipeline, where liquid enters through the side walls in a filtration mode, are investigated. Based on a comparison of analytical dependencies used to describe the flow entry laws into the pipelines in each case, relatively simple and practical calculation formulas have been derived to determine the required degree of the side walls perforation of the drainage pipeline. These formulas ensure that the desired water flow rate is achieved in the collector. The degree of perforation S in this work is defined as the ratio of the area of the perforation holes (slots) in the side walls of the drainage pipeline to the total area of its side surface. In the analysis of the pipelines considered, parameter A is used, which comprehensively accounts for both the design and filtration characteristics of the drainage pipelines. Relevant analytical dependencies and a graph for determining this parameter are presented. A series of calculations have been performed using the proposed formulas to determine the degree of perforation for these pipelines. It is shown that, in general, the magnitude of the perforation degree is influenced by both the structural characteristics of the pipeline itself and the filtration properties of the surrounding soil and the surface of the drainage pipes.

Third harmonic of the dynamic magnetic susceptibility of a concentrated ferrofluid: Numerical calculation and simple approximation formula.

Information about the nonlinear magnetic response of dispersions of magnetic particles is the basis for biomedical applications. In this paper, using analytical and numerical methods, the third harmonic of the dynamic susceptibility of an ensemble of moving magnetic particles in an ac magnetic field with an arbitrary amplitude is studied, taking into account interparticle interactions. A simple approximation formula is proposed to predict the third harmonic as a function of two parameters: the Langevin susceptibility χ_{L}, which is used to estimate the particle dipole-dipole interactions, and the Langevin parameter ξ, which represents the ratio of the energy of the magnetic moment interacting with the magnetic field to the thermal energy. The derived approximation formula corresponds with the known single-particle theories in the limit case of a small particle's concentration and is valid for concentrated dispersions of magnetic particles (with the Langevin susceptibility up to χ_{L}≤3) in high-amplitude ac fields (with the Langevin parameter up to ξ≤10).

Assessment of the Vertical Dimension of Occlusion Using Palm Width and Finger Length.

Background and Objectives: The vertical dimension of occlusion's (VDO) assessment is a highly important issue in the everyday dentist's practice. Patients with unstable occlusion, lost occlusal stops, extensive tooth loss in the lateral area, or complete edentulism need a proper assessment of the VDO before the prosthetic restoration is carried out. Subjective and objective methods were used over time for the restoration of VDO. The study aimed to investigate the possible correlation between finger length, palm width and the vertical dimension of occlusion. Materials and Methods: Assessment of the VDO for 236 subjects, Romanian and French dental students, was performed using the Willis Bite Gauge. The left hand of the subjects was scanned using a flat-bed scanner, and then measurements of palm width and finger length were carried out for each subject. Comparison between VDO values and finger length/palm width was conducted using one-way ANOVA and Student t-Test. Results: Higher VDO average values were found in French subjects compared with Romanian students. The same results were found according to gender; in both female and male subjects, lower values of VDO were found in the Romanian group. Higher values were obtained for women within each group when comparing to men. Statistically significant correlations of the analyzed parameters and VDO values were found. Higher statistical correlations of the studied variables were found for men compared to women in both groups. The highest statistical correlation was obtained between the VDO and the palm width measured at the fingerbase, followed by the middle finger length. Conclusions: The results showed the highest statistical correlation between the vertical dimension of occlusion and the palm width measured at the fingers' base. Statistical correlations were also found between the VDO and the middle finger length. Simple formulas using finger length/palm width can be used for a rapid VDO determination.

Calculations of space-charge tune shifts in storage rings with extremely short bunches and small bunch spacing

Space-charge tune shifts can affect the beam quality in storage rings. Laslett’s method, a classical approach for calculating space-charge tune shifts, may not hold valid assumptions for rings with extremely short bunches and small bunch spacing, such as in steady-state microbunching (SSMB) storage rings. To overcome this limitation, we have developed new formulas that are suitable for arbitrary bunch lengths and spacings for calculating space-charge tune shifts. Additionally, simplified formulas have been provided for the calculations of space-charge tune shifts specifically in the context of extremely short bunch lengths. Numerical computations were carried out to demonstrate the validity of these newly derived formulas. Moreover, the formulas were applied to compute the space-charge tune shifts in an SSMB storage ring characterized by typical parameters. Published by the American Physical Society 2024

Experimental and calculated electronic stopping force determination of 24Cr, 28Ni and 22Ti ions crossing PVC and Mylar foils in the ion energy domain of LSS theory

Energy loss measurements for heavy ions (28Ni,24Cr and 22Ti) crossing thin polymeric foil such as PVC and Mylar in the energy range 0.1–0.3 MeV/n have been carried out utilizing the 6MV Tandem accelerator facility at iThemba-labs in Johannesburg (South Africa). These measurements deduced experimental stopping force data have been compared with those calculated using Lindhard, Scharff and Schiott formulation (LSS) and SRIM-2013 predictions. A large significant deviation has been observed between experimental values and those calculated by LSS formula. Based on physical postulate, we have developed a reasonably simple semi-empirical formula that takes in to account a mean residual projectile charge Z1¯ and suitable ξe factor which depend on Z1 and Z2. This new modified LSS formula has been tested and the calculated stopping force values generated by this formula are in close agreement with the measured ones.

A simplified analytical formula for the coefficient of 3rd-order Hermite moment model and its application

Based on the 3rd-order softened Hermite nonlinear equations, a new simplified formula of the Hermite moment model is proposed. According to the wind tunnel pressure test data of a flat roof, the new and existing simplified formulas are used to calculate the Hermite parameters and peak factors respectively. The calculation accuracies of different simplified formulas are compared and analyzed to verify the applicability of the new simplified formula. The results show that the new simplified formula has higher accuracy for the peak factor calculation of high-order softened time histories, and the relative error is kept within 15%. And the applicability for mild non-Gaussian time histories is relatively better. For low-order softened time histories, the calculation errors of the new simplified formula are relatively large for the Hermite parameters, but the calculation accuracy of the peak factor is kept within the applicable range. Specifically, the calculation errors of the negative peak factors distributed only in the 1st-order softened applicable range are less than 20%, and the calculation errors of the negative peak factors distributed only in the 2nd-order softened applicable range are less than 15%. Finally, the new simplified formula shows good applicability to the extreme value analysis of the high-order and low-order softened wind pressure time histories.

Performance Evaluation of a Simple Strategy to Optimize Formula Constants for Zero Mean or Minimal Standard Deviation or Root-Mean-Squared Prediction Error in Intraocular Lens Power Calculation

PurposeTo investigate the performance of a simple prediction scheme for the formula constants optimized for a mean (MPE), standard deviation (SDPE) or root-mean-squared refractive prediction error (RMSPE). DesignRetrospective cross-sectional study. MethodsUsing IOLMaster 700 biometric data from 888 eyes treated with the Hoya Vivinex lens and 821 eyes treated with the Alcon SA60AT lens, plus the power of the implanted lens and postoperative spherical equivalent refraction, optimized constants for SRKT, Hoffer Q, Holladay 1, Haigis, and K6 formulae were calculated using an iterative nonlinear optimization for zero MPE and minimal SDPE and RMSPE. Start values were detuned by ±1.5 from the MPE optimized constants and formula constants generated using the simple prediction scheme were compared to the corresponding directly optimized constants. ResultsFor all 5 formulae under test and with both datasets, constants optimized using the simple scheme showed excellent agreement with those from the iterative method with either MPE or RMSPE used as the optimization metric, and good agreement with SDPE as the metric. Constants optimized for zero MPE or minimal RMSPE agreed within 0.05, whereas constants for minimal SDPE could be systematically off by up to 0.6 from the MPE values, making SDPE unsuitable as an optimization metric. ConclusionsThis simple formula constant optimization scheme performs excellently for 4 disclosed formulae and one nondisclosed formula in our 2 monocentric datasets with zero MPE or minimal RMSPE as metrics. Multicentric studies with other study populations and biometers are required to further investigate the clinical applicability.

Spatio-Temporal Mechanisms of Rainfall in Kalaburagi District: An Analysis of Trends and Variability

The study used data from 11 taluks to analyse the changes and variability in annual and seasonal rainfall in the Kalaburagi district between 2016 and 2022. Sen Slope and Mann-Kendall analyses were used to evaluate trends, while the coefficient of variation was used to measure rainfall variability. The mean rainfall was calculated using simple mathematical formulas. The findings showed minimal seasonal and yearly variability, with the exception of the southwest monsoon season. The district as a whole as well as all 11 taluks consistently saw a rise in rainfall, according to annual Sen slope research. However, during the northeast monsoon season, negative trends were observed in Aland and Sedam Taluks. In the Mann-Kendall test, the district did not exhibit any general pattern; nevertheless, several taluks, such as Yadrami and Kamalapur, demonstrated remarkable trends in the southwest and northeast seasons, respectively. Due to geographical and climatic fluctuations, the district of Kalaburagi experienced an annual mean precipitation of 797 mm. Higher mean rainfall was recorded in Sedam, Kalagi, Chincholi, and Kamalapur, while lower mean rainfall was recorded in Jevaragi and Yadrami Taluks. In the water-scarce Kalaburagi district, this work is important for policymakers addressing climate change and water resource management.

Spatial-temporal distribution of neglected tropical diseases burdens in China from 2005 to 2020

BackgroundOut of the 21 neglected tropical diseases (NTDs) listed by the World Health Organization, 15 affect the People’s Republic of China. Despite significant achievements in controlling NTDs, comprehensive assessments of the disease burden based on actual case data and detailed information on spatial and temporal dynamics are still lacking. This study aims to assess the disease burden and spatial–temporal distribution of NTDs in China from 2005 to 2020, to provide a reference for the formulation of national health agendas in line with the global health agenda, and guide resource allocation.MethodsThe number of cases and deaths of major NTDs in China from 2005 to 2020 were downloaded from the China Public Health Science Data Center (https://www.phsciencedata.cn/Share/index.jsp) of the Chinese Center for Disease Control and Prevention and relevant literatures. Simplified formulas for disability-adjusted life years (DALYs) helped estimate the years of life lost (YLLs), years lived with disability (YLDs), and total DALYs. Spatial autocorrelation analysis of the average NTDs burden data for the years 2005 to 2020 was evaluated using Moran's I statistic.ResultsChina's overall NTDs burden decreased significantly, from 245,444.53 DALYs in 2005 to 18,984.34 DALYs in 2020, marking a reduction of 92.27%. In 2005, the DALYs caused by schistosomiasis and rabies represent a substantial proportion of the total disease burden, accounting for 65.37% and 34.43% respectively. In 2015, Hunan and Sichuan provinces had the highest diversity of NTDs, with 9 and 8 number of different NTDs reported respectively. And the highest disease burden was observed in Sichuan (242,683.46 DALYs), Xizang Zizhiqu (178,318.99 DALYs) and Guangdong (154,228.31 DALYs). The “high-high” clustering areas of NTDs were mainly in China's central and southern regions, as identified by spatial autocorrelation analysis.ConclusionsChina has made unremitting efforts in the prevention and control of NTDs, and the disease burden of major NTDs in China has decreased significantly. Using the One Health concept to guide disease prevention and control in the field to effectively save medical resources and achieve precise intervention.Graphical abstract

Influence of a Background Shear Flow on Cyclone–Anticyclone Asymmetry in Ageostrophic Balanced Flows

In this paper, we study how cyclonic and anticyclonic vortices adapt their shape and orientation to a background shear flow in an effort to understand geophysical vortices. Here we use a balanced model that incorporates the effects of rotation and density stratification to model the case of an isolated vortex of uniform potential vorticity subjected to a background shear flow that mimics the effect of surrounding vortices. We find equilibrium states and analyze their linear stability to determine the vortex characteristics at the margin of stability. Differences are found between the cyclonic and anticyclonic equilibria depending on the background flow parameters. When there is only horizontal strain, the vertical aspect ratio of the vortex does not change, whereas increasing the imposed background strain rate causes a change in the horizontal cross section, with cyclones being more deformed than anticyclones for a given value of strain. Vertical shear not only causes changes in the vertical axis but also causes the vortex to tilt away from it upright position. Overall, anticyclonic equilibria tend to have a more circular horizontal cross section, a longer vertical axis, and a larger tilt angle with respect to cyclonic equilibria. The strongest asymmetry between the horizontal cross section of cyclonic and anticyclonic vortices occurs for low values of vertical shear, while the strongest asymmetry in the vertical axes and tilt angle occurs for large vertical shear. Finally, by expanding the vortex shape and orientation in terms of the strain rate, we derive simple formulas that provide insights into how the vortex equilibria depend on the background flow.

Urinary metabolic profile and its predictive indexes after MSG consumption in rat.

Monosodium glutamate (MSG) is a widely used food additive with conflicting evidence regarding its potential effects on human health, with proposed relevance for obesity and metabolic syndrome (MetS) or chronic kidney disease. As being able to accurately quantify the MSG dietary intake would help clarify the open issues, we constructed a predictive formula to estimate the daily intake of MSG in a rat model based on the urinary metabolic profile. Adult male Wistar rats were divided into groups receiving different daily amounts of MSG in drinking water (0.5, 1.5, and 3.0 g%), no MSG, and MSG withdrawal after 3.0% MSG treatment for 4 weeks. We then analyzed 24-hour urine samples for chemistries and metabolites using 1H NMR spectrometry and observed a strong correlation between urine pH, sodium, bicarbonate, alpha-ketoglutarate, citrate, fumarate, glutamate, methylamine, N-methyl-4-pyridone-3-carboxamide, succinate, and taurine and the daily MSG intake. Following the multiple linear regression analysis a simple formula model based on urinary Na+, citrate, and glutamate was most accurate and could be validated for estimating daily MSG intake. In conclusion, we propose that the daily MSG intake correlates with urinary metabolites in a rat model and that this new tool for monitoring the impact of MSG on health measures.