Conventional Equation Research Articles

Composite Fermions QED Lagrangian Density in Fractional Formulation

Quantum electrodynamics (QED) is a highly precise and successful theory that describes the interaction between electrically charged particles and electromagnetic radiation. It is an integral part of the Standard Model of particle physics and provides a theoretical basis for explaining a wide range of physical phenomena, including the behavior of atoms, molecules, and materials. In this work, the Lagrangian density of Composite Fermions in QED has been expressed in a fractional form using the Riemann‑Liouville fractional derivative. The fractional Euler-Lagrange and fractional Hamiltonian equations, derived from the fractional form of the Lagrangian density, were also obtained. When α is set to 1, the conventional mathematical equations are restored.

Testing of chlorine dosage in drinking water using microstrip patch sensor

A new method using microstrip patch sensor is designed, simulated, and measured to detect the dosage of added chlorine to the drinking water using the relation between permittivity and matching impedance. The simulation is done using computer simulation technology-microwave studio software. The proposed sensor is designed on a single FR-4 layer with a low profile, 0.499 GHz bandwidth, center frequency of 2.94 GHz, gain of 6.55 dBi, and a good front to back ratio of 17.84 dB. In this work, the antenna design is started from a conventional patch antenna equation. Then, an optimization process is performed to achieve good parameter values for obtaining the desired objective. The objective is to utilize the microwave frequency to measure the chlorine dosage in water. The measurement results proved that the matching impedance can be used to find out the dosage of chlorine in drinkable water. The proposed method overcomes the open-ended coaxial probe method in terms of experimental time and contactless testing and shows high matching with the latter actual data. Moreover, the proposed method overcomes the conventional methods in terms of continuity and large scale of testing, non-contacting with the samples of water, and no additive chemical materials, which make the water samples not drinkable.

Simulation of the coal pyrolysis process in downer reactor with a mass transfer model based on the spatial superposition assumption

A mass transfer model based on the spatial superposition assumption is constructed to investigate the coal pyrolysis process in the downer. The simulated volatiles yield using this developed model are in better agreement with the experimental data than that based on the conventional Jung-La Nauze equation. It is found that the mass transfer coefficients (Kf̅) calculated by the Jung-La Nauze equation are approximately two orders of magnitude higher than that of this work, indicating that the mass transfer process predicted with the uniform structure is overestimated. Moreover, the concentration difference between the surface of dilute particles and gas bulk is small and close to zero, which means that the reaction is the rate controlling step, while the concentration difference between the surface of the clusters and gas bulk is relatively large, which implies that the mass transfer process also becomes the rate controlling step. All these results obtained in this work are expected to deepen the understanding of the mass transfer and reaction process by considering the influence of heterogeneous structures in gas-solid fluidized system.

Beyond fitness: The nature of selection acting through the constructive steps of lifecycles.

We address the problem of defining selection and extracting the adaptive part of evolutionary change, originally formalized by Fisher and Price. Conventionally selection and adaptation are defined through fitness attributed to genes or genotypes chosen as units of selection. The construction through fitness is known to suffer ambiguities and omissions as a theory of change due to selection. We construct an alternative framing in which units of selection and fitness are replaced as the main abstractions by formal lifecycle models and reproduction rates through genetically distinct lifecycle realizations. Graphical representations of lifecycles express relations among reproductive stages that cannot be assigned to any one unit of selection. The lifecycle partition refines the statistics of overall reproductive success and resolves modes of selection that fitness either excludes or distorts through additive projections. We derive the Price equation in the basis of lifecycle realizations and compare it to the conventional Price equation for additive fitness of organisms. We show how the lifecycle approach recovers fitnesses acting concurrently at multiple levels, or contrasts forms of competition within and between levels that are invisible to additive fitness. Defining selection through lifecycles recasts population genetics from an object-focused to a construction- and process-focused representation.

Effect of particle size on the dynamic properties of tire derived aggregates (TDA)

This paper investigates the dynamic properties of tire derived aggregate (TDA) as a recycled material used in civil engineering applications. The effect of TDA type A particle size on the dynamic response is studied experimentally in detail, and the effects of hysteresis loop asymmetry, shear strain, and confining pressure on the shear modulus and damping ratio are also examined. Undrained strain-controlled cyclic triaxial tests with consolidation stresses ranging from 25 to 200 kPa and shear strains ranging from 0.1 to 10% are used to compare a granulated rubber (GR) specimens and TDA specimens with different maximum particle sizes. The dynamic response of TDA type A differs from that of granulated rubber, because of the larger particle sizes of TDA type A. Although TDA stiffness increases with increasing particle size, the damping ratio is insensitive to TDA particle size in the particle size range considered in this study. However, at all consolidation stresses, the damping capacity of GR is significantly lower than that of TDA. In particular, due to hysteresis loop asymmetry, conventional equations can significantly underestimate the shear modulus and damping ratio of TDA type A. Furthermore, a generalized MKZ model is proposed to estimate the maximum shear modulus at small strains (Gmax) and to predict shear modulus degradation curves for TDA type A with maximum particle sizes ranging from 19.1 mm to 50.8 mm. Comparisons of these shear modulus degradation curves to data reported in the literature and to the experimental results of a TDA sample with a random particle size distribution show that the proposed generalized MKZ model can provide reasonable estimates of the shear modulus of TDA type A.

Algorithm for the early prediction of drug stability using bayesian inference and multiple measurements: Application for predicting the stability of silodosin tablets

The stability of active pharmaceutical ingredients (APIs) and formulations has become a major chemistry, manufacturing, and control (CMC) concern in the pharmaceutical industry because it can determine the feasibility of research and development, the development period, and the development costs of a certain formulation. To streamline the research and development of pharmaceutical products and create useful pharmaceutical products at an early stage, a technology that predicts the stability of formulations at an early stage and with a high degree of accuracy is needed. When predicting the stability of a substance, highly reliable data are required; however, the stability data are affected by analytical variations that depend on the experimenter, measurement device, and conditions used. Although these variations greatly affect the prediction accuracy, a stability prediction method that considers these variations has not yet been developed. Here, short-term stability data under accelerated conditions were obtained at three institutions using silodosin tablets as a model sample. By combining Bayesian inference with the temporal change in the amount of the main degradation products obtained and the conventional humidity-corrected Arrhenius equation, we developed a new algorithm that provides a narrow confidence interval, even when using data with variations. By using this algorithm and setting an appropriate number of conditions, we were able to obtain a valid confidence intervals in a short period of time. Here, by performing more measurements than those suggested by the minimum measurement frequency indicated in the guideline specified in the International Council for Harmonisation (ICH) of Technical Requirements for Pharmaceuticals for Human Use, we developed a method that can be used to reasonably predict the long-term stability of the drugs, even if the data measurement interval is short. Our results will help solve various problems in today's pharmaceutical product development scenario and contribute to worldwide health and welfare.

Machine learning-derived low density lipoprotein cholesterol (LDL-C) estimation agrees better with directly measured LDL-C than conventional equations in individuals with type 2 diabetes mellitus.

Searchable abstracts of presentations at key conferences in endocrinology ISSN 1470-3947 (print) | ISSN 1479-6848 (online)

Forecasting of stage-discharge in a non-perennial river using machine learning with gamma test

Knowledge of the stage-discharge rating curve is useful in designing and planning flood warnings; thus, developing a reliable stage-discharge rating curve is a fundamental and crucial component of water resource system engineering. Since the continuous measurement is often impossible, the stage-discharge relationship is generally used in natural streams to estimate discharge. This paper aims to optimize the rating curve using a generalized reduced gradient (GRG) solver and the test the accuracy and applicability of the hybridized linear regression (LR) with other machine learning techniques, namely, linear regression-random subspace (LR-RSS), linear regression-reduced error pruning tree (LR-REPTree), linear regression-support vector machine (LR-SVM) and linear regression-M5 pruned (LR-M5P) models. An application of these hybrid models was performed and test to modeling the Gaula Barrage stage-discharge problem. For this, 12-year historical stage-discharge data were collected and analyzed. The 12-year historical daily flow data (m3/s) and stage (m) from during the monsoon season, i.e., June to October only from 03/06/2007 to 31/10/2018, were used for discharge simulation. The best suitable combination of input variables for LR, LR-RSS, LR-REPTree, LR-SVM, and LR-M5P models was identified and decided using the gamma test. GRG-based rating curve equations were found to be as effective and more accurate as conventional rating curve equations. The outcomes from GRG, LR, LR-RSS, LR-REPTree, LR-SVM, and LR-M5P models were compared to observed values of daily discharge based on Nash Sutcliffe model efficiency coefficient (NSE), Willmott Index of Agreement (d), Kling-Gupta efficiency (KGE), mean absolute error (MAE), mean bias error (MBE), relative bias in percent (RE), root mean square error (RMSE) Pearson correlation coefficient (PCC) and coefficient of determination (R2). The LR-REPTree model (combination 1: NSE = 0.993, d = 0.998, KGE = 0.987, PCC(r) = 0.997, and R2 = 0.994 and minimum value of RMSE = 0.109, MAE = 0.041, MBE = −0.010 and RE = −0.1%; combination 2; NSE = 0.941, d = 0.984, KGE = 0. 923, PCC(r) = 0. 973, and R2 = 0. 947 and minimum value of RMSE = 0. 331, MAE = 0.143, MBE = −0.089 and RE = −0.9%) performed superior to the GRG, LR, LR-RSS, LR-SVM, and LR-M5P models in all input combinations during the testing period. It was also noticed that the performance of the alone LR and its hybrid models (i.e., LR-RSS, LR-REPTree, LR-SVM, and LR-M5P) was better than the conventional stage-discharge rating curve, including the GRG method.

Influence of bimetal interface confinement on the Hall-petch slope of multiscale Cu/Nb multilayer composites

Heterostructured materials afford a new way to improve the mechanical properties, which has become vital in both materials science and engineering applications. In the present research, Cu/Nb multilayer composites with layer thicknesses from the micrometer to nanometer were fabricated by accumulative roll bonding and the microstructure and mechanical properties of the Cu/Nb multilayer composites were then investigated. The yield strength and ultimate tensile strength of these composites increase with decreasing layer thickness. Moreover, the relationship between yield strength and (layer thickness)−1/2 approximately accords with the conventional Hall-Petch equation but with a decrease in the Hall-Petch slope when the layer thickness decreases from the micrometer to nanometer scales. The deformation microstructure of these Cu/Nb multilayer composites clearly exhibit dislocations glide in the layers, which reduces the stacking of dislocations at the Cu–Nb interface and thereby weakens the strengthening effect of the interface.

Thermal Discharge Temperature Retrieval and Monitoring of NPPs Based on SDGSAT-1 Images

High-accuracy sea surface temperature (SST) retrieval near nuclear power plants (NPPs) is one of the most significant indicators for evaluating marine ecological environment quality, monitoring the real-time situation of thermal discharge, and supporting planning decisions. However, complex computations, the inaccessible real-time vertical profile of the atmosphere, and the uncertainty of atmospheric profile data increase the error of SST retrieval. Additionally, influenced by their low spatial resolution, the widely used AVHRR/MODIS remote sensing images (RSIs) are unable to retrieve the detailed distribution of SST in small scale regions such as coastal NPPs. In this paper, we propose a simplified split-window-based temperature retrieval method (the SW method) suitable for SDGSAT-1 30 m thermal infrared spectrometer (TIS) RSIs. Specially, this method only needs atmospheric transmittance and surface emissivity by counteracting the average atmospheric temperature to monitor the thermal discharge of offshore NPPs. First, the geometric and radiometric calibrated thermal infrared and multi-spectral cloudless data of the target regions are selected to obtain the corresponding apparent radiance of the RSIs. Second, in accordance with the red and near-infrared (NIR) bands of multi-spectral RSIs, the surface emissivity is calculated to distinguish water from land. Next, we determine the atmospheric profile parameters from the weather conditions of the target region at the imaging time. Finally, according to the theory of surface-atmosphere radiative transfer, the SST of target regions is retrieved with the proposed SW method, and the results are compared with those of the conventional radiative transfer equation (RTE), mono-window (MW), and the nonlinear sea surface temperature (NLSST) algorithms. The experimental results indicate that the SST retrieved from the split-window algorithms (i.e., SW and NLSST) are generally higher than those of the single-channel algorithms (i.e., RTE and MW). The SST difference between the SW algorithm and the NLSST algorithm is within 0.5 °C. In addition, SDGSAT-1 can monitor the seasonal detailed variation of the thermal discharge near coastal NPPs. This article is the first to attempt to quantitative small-scale SST retrieval based on thermal infrared and multi-spectral images obtained from the SDGSAT-1 TIS and a multispectral imager (MII), and therefore, provide an effective reference for marine environment monitoring.

Calculation of Concentration Distribution of Steady Flow Aerosol by Langevin Dynamics Method

Langevin dynamics (LD) method is a modelling technique using pseudo-random numbers to reproduce the acceleration of aerosol particles due to random collisions of gas molecules onto the particles. Although the LD method can reproduce the Brownian motion of particles and motion due to inertial force and/or external force, it is difficult to understand the behavior of aerosol, which is group of particles, from the information on the motion of individual particles. In this study, a novel calculation method was developed to obtain the concentration distribution of aerosol by accumulating the information of position of particles calculated by the LD method, and it was applied to the diffusion of aerosol flowing steadily in a cylindrical tube. The concentration distribution obtained by this method agreed well with that obtained by solving the conventional convective-diffusion equation. Furthermore, change in cup-mixing concentration of aerosol in axial direction calculated from the concentration distribution agreed well also with the penetration expressed by Gormley & Kennedy.

Kinetics of diffusion-influenced multisite phosphorylation with enzyme reactivation.

The simplest way to account for the influence of diffusion on the kinetics of multisite phosphorylation is to modify the rate constants in the conventional rate equations of chemical kinetics. We have previously shown that this is not enough and new transitions between the reactants must also be introduced. Here we extend our results by considering enzymes that are inactive after modifying the substrate and need time to become active again. This generalization leads to a surprising result. The introduction of enzyme reactivation results in a diffusion-modified kinetic scheme with a new transition that has a negative rate constant. The reason for this is that mapping non-Markovian rate equations onto Markovian ones with time-independent rate constants is not a good approximation at short times. We then developed a non-Markovian theory that involves memory kernels instead of rate constants. This theory is now valid at short times, but is more challenging to use. As an example, the diffusion-modified kinetic scheme with new connections was used to calculate kinetics of double phosphorylation and steady-state response in a phosphorylation-dephosphorylation cycle. We have reproduced the loss of bistability in the phosphorylation-dephosphorylation cycle when the enzyme reactivation time decreases, which was obtained by particle-based computer simulations.

Inclined relative magnetic field analysis of Brinkman type dusty fluid through fluctuating upright parallel plates

Due to the widespread use of magnetohydrodynamic (MHD) in electromagnetic targeted therapy, malignant tumor therapy, magnetic microscopy, regulating blood circulation following operations, and fluid pumping in industrial and technical processes. The main goal of the article investigates the analysis of a dusty Brinkman fluid flowing through fluctuating parallel plates with an inclined relative magnetic field. The study aims to analyze the relative magnetic phenomena which is fixed relative to the fluid (MFFRF) or plate (MFFRP), and its impact on fluid and particle motion. The mathematical modelling of the fluid is established through a conventional partial differential equations, and Buckingham's pi theorem is utilized to obtain dimensionless variables. Poincare-Lighthill perturbation technique (PLPT) is employed to derive the solution, with the aid of the program Mathcad-15, the findings are displayed graphically for both velocities. The study indicates that the relative magnetic field significantly influences fluid and particle motion which can be utilized to control fluid pumping in industrial operations and blood flow during surgery.

Analysis of single-sided ventilation flows of a generic isolated building using particle tracking method in LES simulation

The main objective of this study is to investigate the airflow patterns in single-sided ventilation of isolated buildings in which the ventilation rate can not be easily predicted by the conventional Orifice equation. The research focuses on buildings with two openings located either at the front or back external wall, with building aspect ratios of 1:1 and 1:2.The study utilizes Large Eddy Simulation (LES) with the particle tracking technique validated by velocity data obtained from a wind tunnel experiment. Ventilation performance is evaluated by Airflow Rate (AFR) and Purging Flow Rate (PFR). AFR was obtained based on the instantaneous velocity over the openings, and PFR was determined by the tracer gas method. The results show that the influence of pulsation flow and eddy penetration both exist in single-sided ventilation. The comparison of AFR and PFR indicates part of the airflow through the opening does not contribute to effectively removing the indoor contaminants, which is quantitively evaluated by ventilation efficiency (εv) defined as the ratio of PFR and AFR. In order to explicitly observe and depict the airflow, the massless particles were emitted at the opening, and the trajectories were analysed. The Probability Density Function (PDF) of indoor residence and indoor travel distance was calculated. The high probability of short indoor travel distance and the residence time, which is mainly caused by the eddy at the openings and time-variant pulsation flow, can explain the difference between AFR and PFR.

Solutions to axion electromagnetodynamics and new search strategies of sub-μeV axion

The Witten effect implies the electromagnetic interactions between axions and magnetic monopoles, and the quantum electromagnetodynamics (QEMD) properly describes interactions of electric charges, magnetic charges and photons. Based on the QEMD, a generic low-energy axion-photon effective field theory was built by introducing two four-potentials (Aμ and Bμ) to describe a photon. More anomalous axion-photon interactions and couplings (gaAA, gaBB and gaAB) arise in contrary to the ordinary axion coupling {g}_{agamma gamma}{a F}^{mu nu}{overset{sim }{F}}_{mu nu} . As a consequence, the conventional axion Maxwell equations are further modified. We properly solve the new axion-modified Maxwell equations and obtain the axion-induced electromagnetic fields given a static electric or magnetic field. It turns out that the dominant couplings gaAB and gaBB can be probed in the presence of external magnetic field and electric field, respectively. The induced oscillating magnetic fields are always suppressed compared with the electric fields for the axions with large Compton wavelengths. This is contrary to the situation in conventional experiments searching for the oscillating magnetic fields induced by sub-μeV axions. Thus, we propose new strategies to measure the new couplings for sub-μeV axion in haloscope experiments.

Study on non-Darcian flow and solute transport characteristics through a filled single fracture

ABSTRACT In this study, well-controlled laboratory experiments on flow and solute migration through a Filled-Single Fracture (FSF) of 3 mm aperture size were performed for different flow rates. Non-Darcian flow conditions prevailed throughout the experiment, which can be effectively explained using Forchheimer or Izbash’s equations. The constant mode was utilized to inject a conservative solute (NaCl) evenly through the FSF, following which the resulting Breakthrough curves (BTCs) were developed for three different average flow velocities. The computed BTCs were simulated by the conventional Convection-Dispersion Equation (CDE); and the single rate Mobile-Immobile (MIM) Model. A non-Fickian trend was observed for the attained BTCs, which cannot be interpreted by the Fickian CDE; however, the CDE model serves as the comparing base. MIM model was found much better than the CDE in fitting BTCs for three different average values of pore velocities. Statistical analysis on the goodness-of-fit further confirmed the suitability of MIM as much greater correlation coefficients were observed compared to the CDE model. Further, the BTCs were found to fit better at lower velocities. The greater computed dispersivity values are compatible with Taylor who suggested that much stronger dispersion occurs under non-Darcian flow conditions.

Random forest regression to predict design performance of concert halls

Over the last couple decades, machine learning (ML) and advanced computational strategies have been successful when employed in building physics problems. ML models have known applications in the operations of buildings, including real-time energy monitoring and automated mechanical systems. They can also be used to inform design decisions for complex problems during conceptualization. For acousticians and building designers, trained ML models could provide better insight on expected performance without requiring extensive calculations or room acoustic simulations. This presentation describes a computational method for predicting the design performance (i.e., mid-frequency reverberation time) of various concert halls. More specifically, a random forest (RF) regression model is trained on architectural and measured acoustical data to predict the reverberation time. The RF models are tuned and act as a surrogate model for predicting the mid-frequency reverberation time of concert halls that were not used in model training. The estimated reverberation times are then compared to calculations from conventional equations (i.e., Sabine and Norris-Eyring equations) and room acoustic simulations using ray-tracing methods. This work shows how acousticians and architects can employ ML strategies in the conceptual design phase to improve estimated performance accuracy without expending significant computational resources.

Estimation of in-situ rock strength from borehole geophysical logs in Australian coal mine sites

This study aims to improve the conventional empirical rock strength estimation method that is widely adopted in the Australian coal mining industry and provide more accurate rock uniaxial compression strength (UCS) predictions based on artificial neural network (ANN) models. 274 laboratory-measured UCS data (sample dimension: 60 mm (diameter) × 150 mm (height)) were collected from two longwall coal mines in Australia, along with the four geophysical logs (sonic, gamma, neutron, and porosity logs) and rock density of the tested core specimens. A two-layer ANN model was developed from these data based on the Levenberg–Marquardt algorithm as a base model. As compared to conventional sonic-UCS fitting equations, the mean percentage error, root mean squared error and maximum absolute error of the proposed ANN model were reduced from 34.27%, 15.23 MPa and 70.66 MPa to 20.67%, 11.02 MPa and 47.66 MPa, respectively. Further investigations were conducted by splitting the dataset based on rock lithology and mine locations, and separate ANN models were developed based on the divided subsets. Both lithology-specific and site-specific models exhibited improved estimation accuracy in comparison to the base model, indicating lithology and local geological conditions could considerably affect the estimation accuracy. Among the three types of models, the lithology-specific models yielded the most accurate predictions over the 274 data (MPE: 17.55%; RMSE: 8.84 MPa), followed by the site-specific models and the base model in descending order. Overall, all three models significantly outperformed the current empirical methods adopted in the studied mine sites. The outcomes of this study could provide more accurate UCS predictions for further geotechnical analysis in underground constructions, such as tunnel stability analysis and estimating in-situ stresses based on borehole breakout.

Race-Modified Equations Estimating Renal Function and the Disparity in Partial Nephrectomy Use in Black Patients

Purpose: Black patients with renal tumors are less likely to undergo partial nephrectomy (PN) despite a higher risk of chronic kidney disease (CKD). Racialized equations estimating glomerular filtration rate (eGFR) estimate a 15% to 20% higher renal function for Black patients as opposed to non-Black patients. Whether raced-modified eGFR equations affect the use of nephron-sparing surgery in Black patients has not yet been explored. Materials and Methods: This is a single-center, retrospective review of 6327 consecutive patients who underwent PN (n = 3533) or radical nephrectomy (RN) (n = 2794) from 2005 to 2020. Patients were asked to self-report their race preoperatively. We excluded patients with a tumor thrombus (n = 149). Data were dichotomized into Black patients (n = 654) and non-Black patients (n = 5673). Multivariable logistic regression analysis controlled for known factors associated with PN. The impact of the race-modified (2009CKD-EPI) and race-free (2021CKD-EPI-refit) equations on the distribution of patients across CKD stages was analyzed. Results: Among 6327 patients, 10.3% were Black patients. Black patients had higher comorbidity rates and lower preoperative eGFR than non-Black patients (P < .001). Black patients had lower overall PN rates than non-Black patients (49% vs 57%; P < .001), a finding that was most pronounced in the CKD stage 1 group (55.84% vs 67.43%; P = .0011). On multivariable logistic regression analysis, the Black race was associated with lower odds of PN (OR = 0.76 (0.61-0.96), P = .001). CKD-EPI-refit moved 27% of Black patients to a lower and more accurate CKD stage. Conclusions: Using a conventional race-modified equation potentially overestimated the renal function of 27% of Black patients who were restaged into worse CKD stages when using the race-free equation. While the surgical approach is multifactorial, race-modified equations may overestimate renal function in a significant portion of Black patients and explain some, but not all, of the observed lower utilization of nephron-sparing surgical approaches in Black patients.

Modeling cobalt (III) acetylacetonate and iron (III) acetylacetonate solubilities in supercritical CO2 with PC-SAFT based on experimentally-determined solid–liquid equilibria in organic solvents

A methodology to model the solubilities of metal complexes in supercritical CO2 is indispensable for effectively designing the supercritical CO2-based deposition method. Herein, the solubility of two metal acetylacetonates (acac), Co(acac)3 and Fe(acac)3, in supercritical CO2 was modeled based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and experimentally-determined solid–liquid equilibria in organic solvents. This modeling approach is more predictive than conventional cubic-type equations of state or semi-empirical correlation models. The pure-component parameters of PC-SAFT for metal acetylacetonates are obtained by fitting the obtained solubility data to four typical organic solvents (toluene, acetone, 2-butanone, and ethyl acetate). By applying these PC-SAFT parameters, the model satisfactorily reproduced the solubilities of the metal complexes in supercritical CO2, particularly under low-temperature conditions even with the kij (binary interaction parameter) set to 0 in the combining rule. The isobaric solubilities can also be described by PC-SAFT by generalizing the temperature dependence of kij.