Quartic Model Research Articles

Response Surface Methodology Investigation of the Viscosity of Propylene Glycol (100)/Graphene Nanofluid to Determine the Optimal Conditions

ABSTRACTThis work adopted response surface methodology (RSM) to analyze the behavior of a nanofluid based on propylene glycol. The laboratory conditions in this investigation involve a temperature range of 40°C–120°C and a weight percentage that varies from 0% to 0.5%. Initially viscosity was predicted using Redwood viscometer using the nanofluid solutions. To find the most accurate predictive model and generate an ideal solution, RSM was used. The current study was inspired by the lack of consistency among laboratory behavior and real‐world applications and the statistical‐mathematical analysis of modelers' performance, contrast, and motivations. Two‐factor interaction (2FI), quadratic, cubic, and quartic models are only a few tested. Investigating and evaluating the different statistical features of these modeling functions is a new contribution to the field. The quartic model represents the characteristics of nanofluids with double the accuracy of other models, as shown by statistical analysis. The R2 coefficient, the coefficient of variation (CV%), and the p‐value are compared as metrics for assessing the models. The indexes for the quartic model are 0.9940, 3.53%, and 0.0001, in that order. Nanofluids should have a viscosity of 0.335 m2/s at 120°C along with a weight percentage of 0.5%.

Retrospective analysis of dual-energy x-ray absorptiometry data demonstrates body composition changes with age in dogs and cats.

Use 18 years of dual-energy x-ray absorptiometry (DEXA) scan data to characterize how body composition changes with age in dogs and cats. This was a retrospective observational study using data obtained from DEXA scans performed between 2006 and 2023. A total of 6,973 observations from 1,273 colony-housed dogs ≤ 1 to 16.1 years old and 6,593 observations from 1,096 colony-housed cats ≤ 1 to 16.9 years old were obtained. Animal ages were rounded to the nearest 1/10-year intervals. Means for each interval were calculated and quadratic, cubic, and quartic polynomial models were fit to assess trends over age. Age had an effect on all DEXA measurements. In dogs, lean mass increased early in life before slowing to a peak at age 6.3 and then declined gradually. Fat mass also increased until slowing to a peak at age 9.3 and then decreased. In cats, lean mass increased before slowing to a peak at age 4.5, decreased gradually until age 12.5, and then sharply declined. Fat mass increased until slowing to a peak at age 7.5 and then decreased gradually. This retrospective study provides a baseline for how body composition changes with age. Results suggest that lean mass loss may begin earlier than previously reported in dogs and cats. Sarcopenia and obesity are common conditions in aging pets. Results can be used to improve body composition assessment of patients and investigate the efficacy of nutritional interventions.

Blobbed topological recursion of the quartic Kontsevich model II: $\mathrm{Genus}=0$ (with an appendix by Maciej Dołęga)

We prove that the genus-0 sector of the quartic analogue of the Kontsevich model is completely governed by an involution identity which expresses the meromorphic differential \omega_{0,n} at a reflected point \iota z in terms of all \omega_{0,m} with m\leq n at the original point z . We prove that the solution of the involution identity obeys blobbed topological recursion, which confirms a previous conjecture about the quartic Kontsevich model.

Simulating a numerical UV completion of quartic Galileons

The Galileon theory is a prototypical effective field theory that incorporates the Vainshtein screening mechanism—a feature that arises in some extensions of general relativity, such as massive gravity. The Vainshtein effect requires that the theory contain higher order derivative interactions, which results in Galileons, and theories like them, failing to be technically well posed. While this is not a fundamental issue when the theory is correctly treated as an effective field theory, it nevertheless poses significant practical problems when numerically simulating this model. These problems can be tamed using a number of different approaches: introducing an active low-pass filter and/or constructing a UV completion at the level of the equations of motion, which controls the high momentum modes. These methods have been tested on cubic Galileon interactions, and have been shown to reproduce the correct low-energy behavior. Here we show how the numerical UV-completion method can be applied to quartic Galileon interactions, and present the first simulations of the quartic Galileon model using this technique. We demonstrate that our approach can probe physics in the regime of the effective field theory in which the quartic term dominates, while successfully reproducing the known results for cubic interactions. Published by the American Physical Society 2024

Scalar radiation with a quartic Galileon

The class of Galileon scalar fields theories encapsulate the Vainshtein screening mechanism, which is characteristic of a large range of infrared modified theories of gravity. Such theories can lead to testable departures from general relativity through fifth forces and new scalar modes of gravitational radiation. However, the inherent nonlinearity of the Vainshtein mechanism has limited analytic attempts to describe Galileon theories with both cubic and quartic interactions. To improve on this, we perform direct numerical simulations of the quartic Galileon model for a rotating binary source and infer the power spectrum of given multipoles. To tame numerical instabilities we utilize a low-pass filter, extending previous work on the cubic Galileon. Our findings show that the multipole expansion is well defined and under control. Moreover, our results confirm that despite being a nonlinear scalar, the dominant Galileon radiation is quadrupole, and we find a new scaling behavior deep inside the Vainshtein region. Published by the American Physical Society 2024

Optimization of formulation and processing conditions for the production of functional noodles containing orange-fleshed sweet potatoes and biofortified beans.

The global demand for noodles continues to increase due to their convenience, wide appeal, and affordability. Instant noodles, in particular, are popular for their easy preparation. With annual consumption reaching 106 billion servings in 2019, there is a growing awareness of the importance of healthy food options. However, most noodle types currently available commercially are of low nutritional value. This study sought to develop a protocol for the production of functional noodles consisting of orange-fleshed sweet potatoes (OFSP) puree and biofortified bean powder (BBP). Response surface methodology (RSM) was used to optimize product formulation and processing parameters. Reduced quartic models were found to adequately represent the relationship between dependent variables (hardness, moisture, protein, dietary fiber, iron, and zinc content) and independent variables (dough thickness, drying temperature, and drying time). R 2 values were 0.86-0.99, with a nonsignificant lack-of-fit (p < .05). Using numerical optimization, the optimal protocol for the production of functional noodles was determined to include formulation consisting of wheat 73%, OFSP 21.5%, and BBP 5.5%; dough thickness of 2.0 mm; drying temperature and time of 80.0°C and 143.4 min, respectively. These conditions yielded noodles with 5.9% moisture, 11.0 N hardness, 34.5% protein, 11.9% dietary fiber, 86.9 ppm (parts per million) iron, and 50.53 ppm zinc, with a desirability value of 0.82. Experimental validation demonstrated no significant difference from predicted values. Sensory evaluation rated the noodles as acceptable to consumers, with an overall acceptability of 7.8 on a 9-point hedonic scale. These results show the potential of OFSP and BBP as ingredients for acceptable and nutrient-rich noodles.

Frequency Response Informed Order Reduction Approaches for Pseudo-2D Model for Li-Ion Batteries

To simulate the battery performance quickly using the P2D model,1,2 various simplifications and mathematical reformulations are introduced. One such simplification is the polynomial profile approximation in the solid phase. Such simplifications result in a significant reduction in the simulation time while having a minor compromise in the accuracy, especially for highly fluctuating currents. Building on the previous work by Subramanian et al.,3,4 in this presentation, the Hexic profile polynomial approximations are proposed. The frequency response-based criteria were used to derive the optimal coefficients which give rise to the best possible Hexic model for a given family of current profiles.5 Compare to the Quartic model (QP) based simplifications, the proposed Hexic model (HP) provides comparable computational time (t sim) but offers a factor of 3 improvements in the average error in the cell voltage calculation (εavg [mV]). However, compared to the fully converged FD model, it offers significant improvement in computational time at the cost of 0.5 mV average error in the cell voltage (see Figure 1).In the context of the P2D model, Hexic profile-based solid phase concentration treatment leads to much better prediction (compared to the parabolic and quartic profiles) of the internal variables such as current distribution in electrodes and the stress distribution (radial and tangential stresses inside the solid particles) generated during lithiation and de-lithiation process.The presentation will also discuss critical comparison between the global polynomial-based models (orthogonal collocation and Galerkin approaches) and the frequency domain-based approaches.References Doyle, T. F. Fuller, and J. Newman, J Electrochem Soc, 140, 1526 (1993).Newman and K. E. Thomas-Aleya, John Wiley & Sons, New Jersey (1991).R. Subramanian, J. A. Ritter, and R. E. White, J Electrochem Soc, 148, E444 (2001).R. Subramanian, V. D. Diwakar, and D. Tapriyal, J Electrochem Soc, 152, A2002 (2005).Mishra, V. R. Subramanian and B. Suthar, J Electrochem Soc, 169 (12), 120532 (2022). Figure 1

Presenting a model based on knowledge management in modeling and optimizing the dynamic viscosity of MWCNT (30%) - ZnO (70%) / SAE 40 oil hybrid nano-lubricant with response surface methodology (RSM) for industrial uses

Thermophysical characteristics of MWCNT-ZnO (30–70%)/SAE40 hybrid nanofluid (HNF) using knowledge management cycle and RSM in different solid volume fractions (SVFs), temperature and shear rates (SRs) have been investigated. Emphasis on knowledge management through the use of fast and high-precision methods has led to the use of the RSM for modeling the viscosity of HNF. Different models such as linear model, 2FI, Quadratic, Cubic, Quartic, Fifth and Sixth models are presented. Fifth order model is better than others. Values of R2, Predicted R² and Adjusted R² for all three parameters are 0.9998, which displays good precision of the modeling. The knowledge management cycle is used to evaluate the model to increase sufficient confidence. Examining the matching graphs, deviation coefficient and standard deviation parameters displays good precision of modeling. MOD value is also within ± 2%. With the help of knowledge management in finding the best mode, the optimal viscosity value is equal to 209.53 mPa.sec in temperature, SVF and SR, respectively 31.156 °C, 0.063 % and 933.923 s−1.

Duality of O(N) and Sp(N) random tensor models: tensors with symmetries

In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far in the literature had no symmetry under permutation of the indices. In this paper, we generalize these results for tensors models with interactions of arbitrary order which further have non-trivial symmetry under the permutation of the indices. Totally symmetric and anti-symmetric tensors are thus treated as a particular case of our result.

Presenting the best correlation relationship for predicting the dynamic viscosity of CuO nanoparticles in ethylene glycol -water base fluid using response surface methodology

The types of correlation relationships by different models for predicting of the dynamic viscosity of CuO nanoparticles (NPs) in the ethylene glycol (EG) (80 %)-Water (20 %) base fluid (BF) by using response surface methodology (RSM) statistical method under temperature conditions of T = 15 to 50 °C, solid volume fractions of SVF = 0.05 to 1 % and shear rate SR = 26.6 to 933.1 s−1 were investigated. Models of Quadratic, Cubic, 2FI and Quartic were investigated. These different models were analyzed based on the measurement criteria such as Correlation deviation, coefficient of determination, standard deviation, reliability and P-values; there are important parameters that were used to compare the models. Among these four models, the Quartic model has been chosen as superior model and used to optimize nanofluid (NF) viscosity. The optimization was done in cold environmental conditions and SVF, T, SR variables and viscosity were selected as minimum values and applied to the system. In the conditions of T = 25.303 °C, SVF = 0.05 % and SR = 26.660 sec-1, most optimal NF viscosity value was 8.565 mPa.sec.

On the Quartic Korteweg–de Vries hierarchy of nonlinear Rossby waves and its dynamics

A long-standing challenge in exploring the dynamics of large-scale atmospheric or oceanic motions is to find more appropriate theoretical models. This paper aims at the mechanisms of nonlinear Rossby waves by a new obtained nonlinear evolutionary equation hierarchy approach. The multiple scales method and weak nonlinear perturbation method are adopted based on the quasi-geostrophic potential vorticity conservation law for large scale atmospheric or oceanic motions. It is the first time that a Quartic Korteweg–de Vries model equation is derived to describe the propagation of nonlinear Rossby waves amplitude, which provides a new acceptable theoretical model for the study of atmospheric blocking phenomena. Qualitative and quantitative analysis for the new Quartic KdV model are finished to disclose the evolutionary mechanisms of nonlinear Rossby waves. The corresponding results declares that the β effect, topographic features and detuning parameter are all important factors on the nonlinear Rossby waves.

Optimization of synergistic extraction of calcium ion via an emulsion liquid membrane using dicyclohexano-18-crown-6 and D2EHPA carriers: A design of experiment study

Calcium ions play an important role in various fields, with their stable isotopes being of particular importance in medical research and in the production of superheavy metals. Emulsion liquid membranes (ELMs) offer a promising alternative to conventional methods for metal ion extraction due to their remarkable mass transfer rates. However, the effectiveness of crown ethers as carriers in ELM processes has been hindered by their limited ability to extract calcium ions. The aim of this study is to optimize the extraction of calcium ions using an ELM containing dicyclohexano-18-crown-6 (DC18C6) as a carrier and di-(2-ethylhexyl) phosphoric acid (D2EHPA) as a synergistic carrier. To achieve this objective, a two-level fractional factorial design (FFD) was initially implemented to screen the key factors. Subsequently, a central composite design (CCD) was employed to optimize the four identified key factors. The CCD method yielded a quartic regression model for calcium extraction efficiency. The optimum values were: DC18C6 concentration at 0.035 mol/L, feed phase pH of 4, a feed/emulsion volume ratio of 2.3, and a W/O/W stirring time of 23.4 min. Under these optimal conditions, DC18C6 exhibited negligible extractability, while D2EHPA achieved an extraction efficiency of 62.2%. Combining both carriers, however, significantly increased the extraction efficiency to 97.3%, indicating a synergistic effect that enhanced the extraction of Ca(II) ions. Furthermore, the selectivity of the ELM towards Ca(II) ions was examined in binary solutions of Ca(II)/Li(I), Ca(II)/Na(I), and Ca(II)/Mg(II). The ELM demonstrated selectivity for Ca(II) over Li(I), Na(I), and Mg(II) with separation factors of 4.4, 2.0, and 8.1, respectively. It is noteworthy that the combination of carriers positively influenced calcium selectivity exclusively in the Ca(II)/Mg(II) solution. Conversely, no noticeable effect on selectivity was observed in the Ca(II)/Li(I) solution, while the combination had an adverse effect on calcium selectivity in the Ca(II)/Na(I) solution.

Microwave-assisted acidic hydrolysis of phytate from rye bran – Experimental procedure and model prediction

Phytate is an abundant phosphorus (P) compound in plant material, which cannot be taken up by monogastric animals but is to a significant part released into the environment with excreta. In order to make use of cereals' phytate content, phytate hydrolysis by microwave-assisted thermal treatment of an acidic rye bran extract into inorganic phosphate was investigated experimentally and by modelling for process application. A phytate conversion of 98.5% could be achieved at 200 °C and 15 min reaction time and showed to be highly dependent on the temperature by a sigmoidal correlation. Treatment time showed its main influence in the mid temperature range (between 150 and 180 °C), thus didn't play a role anymore at beginning hydrolysis and towards full conversion. A mathematical quartic model represented phytate conversion with an optimum at harshest examined conditions and allows for predictions of the hydrolysis within the parameter range investigated. A kinetic model gives parameters of reaction order 0.68 and an activation energy of 118.7 kJ/mol with the option to predict phytate hydrolysis beyond the investigated parameter range and for varying input concentration. Equal liberation of all six phosphate groups from phytate is mechanistically suggested. Both model approaches show comparable results.

Phase diagram and topological expansion in the complex quartic random matrix model

AbstractWe use the Riemann–Hilbert approach, together with string and Toda equations, to study the topological expansion in the quartic random matrix model. The coefficients of the topological expansion are generating functions for the numbers of 4‐valent connected graphs with j vertices on a compact Riemann surface of genus g. We explicitly evaluate these numbers for Riemann surfaces of genus 0,1,2, and 3. Also, for a Riemann surface of an arbitrary genus g, we calculate the leading term in the asymptotics of as the number of vertices tends to infinity. Using the theory of quadratic differentials, we characterize the critical contours in the complex parameter plane where phase transitions in the quartic model take place, thereby proving a result of David. These phase transitions are of the following four types: (a) one‐cut to two‐cut through the splitting of the cut at the origin, (b) two‐cut to three‐cut through the birth of a new cut at the origin, (c) one‐cut to three‐cut through the splitting of the cut at two symmetric points, and (d) one‐cut to three‐cut through the birth of two symmetric cuts.

Experimental analysis and response surface optimization of the influence of Zn/Al mass ratio on the creep resistance and tensile properties of As-cast Mg-Zn-Al alloy

Mg-Zn-Al (ZA) alloys are intended to exhibit creep resistance and high temperature mechanical capabilities due to appropriate Zn/Al mass ratio control. The effect of altering Al concentration (1, 2, 3, 4, 5, 6) on the tensile and creep resistance properties of Mg-9Zn-xAl alloy was determined experimentally and quantitatively optimized using response surface method (RSM). It was observed that 2 wt% Al improves both room and elevated temperature tensile strength, and ductility of the considered ZA alloy. The creep rate sharply increased when the mass fraction of aluminum rose above 4 wt%. For the purpose of forecasting the tensile and creep properties of the ZA alloy at any given aluminum mass percentage, quartic models were generated, with all model terms significant. Strong room and high-temperature tensile strength, %elongation, and creep resistance were all reached in the low Al-containing ZA alloys, with 1.597 wt% anticipated ideal Al mass concentration, according to RSM optimization.

Nonlinear computational framework for hybrid ductile glulam joists

This paper starts by presenting a nonlinear algebraic analysis of hybrid glulam sections, including ductile compression-softening constitutive models obtained via regression analysis of material test data, to compute full-range admissible values of moment (M), co-existent curvature (κ) and excluded-area axial force (Fea) for the sections. The (M,κ,Fea) states, double-checked by treating the section alternately as discretised and as a continuum, are clustered into (M,κ) and (M,Fea) data-sets that permit regression-analysis of κ and Fea as polynomial functions of M. For any load on a glulam member the M profile is known, so κ(M) is a more efficient route to calculating deflections than is M(κ). The κ(M) and Fea(M) constitutive functions, which enable assessment of any section state without tedious recalculation, are fused with longitudinal compatibility and equilibrium requirements to predict the joists’ nonlinear responses up to ultimate. Using quartic or Glos compressive constitutive models, spreadsheet-coding of this framework is shown to predict nonlinear local (κ(M)) and global (load–deflection) responses close to test data, also axial and longitudinal-shear stress redistributions mimicking FE predictions for distributed- or point-loaded hybrid glulam joists comprising combinations of poplar, blue-gum, maritime-pine and larch. The results show that post-peak reductions on compressive stress–strain curves cause through-depth reversal of longitudinal-shear at high moments.

Modelling the effects of mixing ratio and temperature on the thermal conductivity of GNP-Alumina hybrid nanofluids: A comparison of ANN, RSM, and linear regression methods

This research aimed to evaluate and compare the efficacy of three distinct methods for forecasting the thermal conductivity of GNP-Alumina hybrid nanofluids. The methods under consideration were artificial neural network (ANN), response surface methodology (RSM), and linear regression (LR). The predictive performance of the ANN model was investigated in relation to the number of neurons in the hidden layer. The findings revealed that the optimal number of neurons was 7, which produced the best performance with an overall mean square error (MSE) of 1.08E-06. The correlation coefficient was also high at 0.99799. The RSM approach involved testing linear, quadratic, cubic, and quartic models, with the quadratic model showing the highest predicted R2 (0.9721) values, indicating that it provided the best fit to the data. Finally, the LR model was developed using a backward elimination approach, with temperature and volume fraction being the significant variables in the final model. Overall, the ANN model produced the most accurate predictions, followed by the RSM and LR models. These findings suggest that the ANN and RSM techniques can be effective tools for forecasting the thermal conductivity of nanofluids, and highlight the importance of selecting appropriate model parameters for optimal performance.

Inverse problem for the quartic mean-field Ising model

Inverse problem for the quartic mean-field Ising model

Reconstruction of spatially continuous time-series land subsidence based on PS-InSAR and improved MLS-SVR in Beijing Plain area

ABSTRACT Beijing has undergone severe settlement in recent years. Persistent Scatterers Interferometric Synthetic Aperture Radar (PS-InSAR) technique has been widely used to derive time-series land deformation. However, existing studies have faced two challenges: (1) the nonlinear characteristics of time-series subsidence has not been fully investigated; (2) since PS points are normally distributed in urban areas with high building density, measurement gaps usually exist in nonurban areas. To address the challenges, we presented a new method to reconstruct spatially continuous time-series deformation. First, PS-InSAR was used to retrieve the deformation based on 135 scenes of Envisat ASAR and Radarsat-2 images from 2003 to 2020. Polynomial Curve Fitting (PCF) was then used to model nonlinear time-series deformation for the PS points. In the PS measurement gaps, Iterative Self-Organizing Data Analysis Technique (ISODATA) and Multi-output Least Squares Support Vector Regression (MLS-SVR) were used to estimate the PCF coefficients and then time-series deformation considering 40 features including thickness of the compressible layers, annual groundwater level, etc. The major results showed that (1) compared to linear, quadratic, and quartic models, cubic polynomial model generated better fit for the time-series deformation (R2 ≈0.99), suggesting obvious nonlinear temporal pattern of deformation; (2) the time-series deformation over measurement gaps reconstructed by ISODATA and MLS-SVR had satisfactory accuracy (R2 = 0.92, MAPE < 15%) and yielded higher accuracy (R2 = 0.947) than IDW (R2 = 0.687) and Ordinary Kriging (R2 = 0.688) interpolation methods. The reconstructed results maintain the nonlinear characteristics and ensure the high spatial resolution (120 m) of time-series deformation. Among the 40 predictor variables, ground water level datasets are the most influential predictors of time-series deformation.

Investigating the effect of different parameters on the rheological behavior of hybrid nano-lubricant containing MWCNT and CuO nanoparticles using response surface methodology (RSM)

In this study, changes in the viscosity of MWCNT-CuO (40%-60%)/ 10 W40 hybrid nano-lubricant (HNL) were modeled and evaluated with the influence of independent parameters using response surface methodology (RSM). RSM with statistical mathematical techniques and appropriate modeling is one of the best methods for evaluating changes in viscosity in terms of independent parameters. Independent and effective parameters on viscosity include temperature (T), solid volume fraction (SVF) and shear rate (SR). Viscosity changes were investigated by presenting different models using 174 laboratory data and the best model among the different models with three parameters T, SR and SVF was introduced. The accuracy of the models was checked with R2, Adjusted R2, and Predicted R2 parameter values. The three-parameter model with parameter values R2 = 0.9992 Adjusted R2 = 0.9990 and Predicted R2 = 0.9986 has higher accuracy than other models. Using the optimal model, the process of viscosity changes was analyzed and investigated, and after evaluating the independent parameters, it was found that the effect of T on viscosity is greater than other parameters. The SR parameter has the least effect on viscosity changes. Also, the normal scatter diagram for the Quartic model for viscosity in terms of T, SVF and SR parameters is close to the bisector line and does not need a transfer function. The graph of the residual values according to the predicted values is in the range between + 3.7 and −3.7. Tthis shows that the accuracy of the selected model is satisfactory.