Law Equation Research Articles

Joule Effect in Electrically Aligned CNFs: Toward Fast Heating of Liquids

Efficient use of heating systems is necessary from an environmental and economic perspective. This work analyses the Joule effect and the thermal transport properties of carbon nanofibers dispersed in ethylene–glycol aligned by applying a constant AC electric field. We tested several weight fraction concentrations from 0.1 % to 1 % wt of carbon nanofibers. The evolution of temperature and electric current as a function of time was analyzed. The amount of heat generated was quantified using Joule's law equation, and we estimated the thermal conductivity as a function of the concentration before and after the voltage application. The dependence of the temperature increase on the concentration of carbon nanofibers and electric voltage was investigated. Our work explores the viability of using carbon nanofiber dispersed in ethylene glycol in developing intelligent fluids useful for heat generation and release, with applications in heat management systems, such as those used for deicing.

Modified Green-Ampt model for infiltration analysis in loess area and its parameter determination and verification

Water infiltration into soil is important in geotechnical engineering. The classical Green-Ampt (GA) infiltration model is widely used in soil infiltration due to its physical significance, but it ignores the actual unsaturated layer in the infiltration process and has some deficiencies. Thus, the present study established a modified GA infiltration model (MLGA model) using Darcy’s infiltration law and continuity equation to fully consider the variation characteristics of the soil water profile in the infiltration process. The Philip model and the GA model have the same physical basis. By combining the internal relationship between the infiltration rate and cumulative infiltration of the two models, the expression of matrix suction of the MLGA model was obtained. The existing measured data was used to verify the correctness and applicability of the MLGA model. Finally, the sensitivity analysis of the critical parameters of the model was performed. The results showed that the MLGA model is reliable and can be used for water infiltration analysis in loess sites. When the MLGA model is used to calculate the infiltration depth, the maximum relative error between the calculated value and the measured data is less than 10%, and the average relative error is 5.54%, which indicates that the model has a high calculation accuracy. The average error of the MLGA model is 24.47% of the Kostiakov model and 80.42% of the existing modified GA model (LGAM model). Sensitivity analysis of the saturated permeability coefficient, initial water content, saturated water content, and matrix suction was performed using the single-factor disturbance method. The influence of each parameter on infiltration depth was summarized, and the sensitivity of each parameter was quantitatively evaluated, which revealed that saturated water content is a highly sensitive parameter. When using the MLGA model to calculate infiltration depth, the accuracy of saturated water content should be ensured first. Finally, the difference between the MLGA model and the LGAM model in describing the whole process of water infiltration is discussed, and the influence mechanism of critical parameters on the water infiltration process is deeply analyzed. The established MLGA model provides theoretical support for further study of the loess water infiltration mechanism.

Positivity-preserving pseudo arc-length method for solving extreme explosive shock wave flow field problems in hyperbolic conservation law equations

Positivity-preserving pseudo arc-length method for solving extreme explosive shock wave flow field problems in hyperbolic conservation law equations

Theoretical Calculation and Simulation of Peak Distortion of Absorption Spectra of Complex Mixtures.

Attenuated total reflection (ATR) spectroscopy in infrared is a standard tool used in most analytical labs, as it allows a rapid chemical analysis with virtually no sample preparation. However, when the sample contains materials with a high refractive index, special care must be taken as the resulting data may be severely biased. This article reports a theoretical approach to correcting distorted ATR spectra. Starting from Snell's law, Lorenz model and Fresnel's equations are combined to obtain the complex relationship between optical constants. With calculating the real and imaginary parts, that is, and , respectively, of the complex refractive index from the absorption spectrum, a model for mixtures comprising of a liquid and a solid is established. The effects of distortion and potential misinterpretation of the data are discussed. Proof-of-concept experiments with mixtures of carbonaceous materials and toluene confirm the theoretically predicted observations.

Comparing Melting Curves of Metals Using the Equation of State and Lindemann's Law

Comparing Melting Curves of Metals Using the Equation of State and Lindemann's Law

Kinetics of hydrothermal reactions of n-butanol over Pt/Al2O3 catalyst for biopropane fuel gas production

Energy defossilisation using drop-in biofuels is an important step towards Net Zero. Producing low-carbon clean-burning propane fuel from biomass provides such additional sustainability benefits. In this work, kinetics of hydrothermal reactions of n-butanol, a biomass-derived feedstock, to produce propane over 5 wt% Pt/Al2O3 catalyst have been studied from 523- 573 K. Experimental data revealed negligible internal and external mass transfer effects and, when fitted to an integral power-rate law equation, gave activation energy of 70 kJ mol−1 (n-butanol reaction order = 1). Furthermore, an appropriate Langmuir-Hinshelwood model was developed, which predicted similar activation energy 62 kJ mol−1. Low adsorption enthalpies for n-butanol (–33.51 kJ mol−1) and water (−18.16 kJ mol−1) indicated weak interactions on the catalyst surface. These agreed with the fast reaction rate of ≈1.0 x 10-5 mol gcat-1 s−1 obtained at ≥ 548 K. As a new research area, generation of such accurate kinetics data will contribute to process development for large-scale biopropane production.

Effect of the Ratio of Protein to Water on the Weak Gel Nonlinear Viscoelastic Behavior of Fish Myofibrillar Protein Paste from Alaska Pollock.

The linear and nonlinear rheological behaviors of fish myofibrillar protein (FMP) paste with 75%, 82%, and 90% moisture content were evaluated using small-amplitude oscillatory shear (SAOS) and large-amplitude oscillatory shear (LAOS) tests. SAOS revealed pastes with 75% and 82% moisture exhibited solid-like behavior, characterized by higher storage modulus (G') than loss modulus (G″), indicative of weak gel properties with a strong protein interaction. In contrast, the 90% moisture content showed more viscous behavior due to weakened protein-protein entanglements. The frequency exponent (n' and n″) from the power law equation varied slightly (0.24 to 0.36), indicating limited sensitivity to changes in deformation rate during SAOS. LAOS tests revealed significant structural changes, with Lissajous-Bowditch curves revealing early nonlinearities at 10% strain for 90% moisture content. Decomposed Chebyshev coefficients (e3/e1, v3/v1, S, and T) indicated strain stiffening at lower strains for the 75% and 82% moisture pastes (i.e., < 50% strain for 75% and < 10% strain for 82%), transitioning to strain thinning at higher strains. Additionally, numerical model confirmed the predictability of the 3D printing process from the nonlinear rheological data, confirmed the suitability of the 75% and 82% moisture pastes for applications requiring structural integrity. These insights are essential for optimizing processing conditions in industrial applications. The findings suggest that the 75% and 82% moisture pastes are suitable for applications requiring structural integrity, while the 90% moisture paste is ideal for flow-based processes. These insights are essential for optimizing processing conditions in industrial applications.

Physics informed neural network can retrieve rate and state friction parameters from acoustic monitoring of laboratory stick-slip experiments

Various machine learning (ML) and deep learning (DL) techniques have been recently applied to the forecasting of laboratory earthquakes from friction experiments. The magnitude and timing of shear failures in stick-slip cycles are predicted using features extracted from the recorded ultrasonic or acoustic emission (AE) signals. In addition, the Rate and State Friction (RSF) constitutive laws are extensively used to model the frictional behavior of faults. In this work, we use data from shear experiments coupled with passive acoustic (variance, kurtosis, and AE rate) interleaved with active source ultrasonic monitoring (transmitted wave amplitude) to develop physics-informed neural network (PINN) models incorporating the RSF law and AE rate generation equation with wave amplitude serving as a proxy for friction state variable. This PINN framework allows learning RSF parameters from stick-slip experiments rather than measuring them through a series of velocity step experiments. We observe that when the stick-slip cycles are irregular, the PINN models outperform the data-driven DL models. Transfer learning (TL) PINN models are also developed by pre-training on data collected at one normal stress level followed by forecasting shear failures and retrieving RSF parameters at other stress levels (i.e., with different recurrence intervals) after retraining on a limited amount of new data. Our findings suggest that TL models perform better compared to standalone models. Both standalone and TL PINN-estimated RSF parameters and their ground truth values show excellent agreements thus demonstrating that RSF parameters can be retrieved from laboratory stick-slip experiments using the corresponding acoustic data and that the transmitted wave amplitude provides a good representation of the evolving frictional state during stick-slips.

Are Wild Prey Sufficient for the Top Predators in the Lowland Protected Areas of Nepal?

A balanced equilibrium between carnivores and their prey is crucial for maintaining ecosystem sustainability. In this study, we applied the predator-prey power law equation to assess the balance between the biomass densities of carnivores and their wild prey within Nepal's lowland protected areas during 2013, 2018, and 2022. The estimated value of the power law exponent k for predator-prey biomass was 0.71 (95% CI = 0.39-1.05), indicating an approximate threefold increase in predator biomass density for every fivefold increase in prey biomass density. Consequently, this creates a systematically bottom-heavy predator-prey biomass pyramid. This finding, consistent with the k = 3/4 trophic biomass scaling across ecosystems, suggests that predator biomass is proportionally sustained by prey biomass, indicating a balance between top predators and their wild prey in Nepal's lowland protected areas. We further demonstrated it is possible to retain the overall power law exponent while jointly measuring intraguild competition between two predators with canonical correlation analysis. This understanding opens avenues for future research directed toward unraveling the factors that drive these consistent growth patterns in ecological communities.

A New Second-order Maximum-principle-preserving Finite-volume Method for Flow Problems Involving Discontinuous Coefficients

A new development of Finite Volumes (FV, for short) and its theoretical analysis are the purpose of this work. Recall that FV are known as powerful tools to address equations of conservation laws (mass, energy, momentum,...). Over the last two decades investigators have succeeded in putting in place a mathematical framework for the theoretical analysis of FV. A perfect illustration of this progress is the design and mathematical analysis of Discrete Duality Finite Volumes (DDFV, for short). We propose now a new class of DDFV for 2nd order elliptic equations involving discontinuous diffusion coefficients or nonlinearities. A one-dimensional linear elliptic equation is addressed here for illustrating the ideas behind our numerical strategy. The algebraic structure of the discrete system we have got is different from that of standard DDFV. The main novelty is that the so-called diamond mesh elements are confined in homogeneous zones for flow problems governed by piecewise constant coefficients. This is got from our judicious definition of the primal mesh. The gain is that there is no need to compute homogenized coefficients to be allocated to the so-called diamond cells as required to conventional DDFV. Notice that poor homogenized permeability allocated to diamond elements leads to poor approximations of fluxes across grid-block interfaces. Moreover for 1-D flow problems in a porous medium involving permeability discontinuities (piecewise constant permeability for instance) the proposed FV scheme leads to a symmetric positive-definite discrete system that meets the discrete maximum principle; we have shown its second order convergence under relevant assumptions.

A comprehensive kinetic modeling study on NH3/H2, NH3/CO and NH3/CH4 blended fuels

Ammonia (NH3), as an ideal zero-carbon fuel, plays a positive role in mitigating global warming. By cofiring NH3 with highly reactive small molecule fuels such as hydrogen (H2), carbon monoxide (CO) and methane (CH4), the reactivity of NH3 combustion can be significantly enhanced. In this work, a detailed kinetic mechanism for NH3/CH4/H2/CO containing 146 species and 1099 reactions was developed and extensively validated with selected experimental data from the literature on laminar burning velocity (LBV), ignition delay time (IDT), and species concentrations measured in burner-stabilized flames (BSF), plug flow reactors (PFR) and jet-stirred reactors (JSR), covering temperatures of 273–2000 K, pressures of 0.053–40 atm and equivalence ratios of 0.1–2. In addition, the detailed mechanism was simplified to include 53 species and 353 reactions using three simplification methods. Kinetic modeling analysis showed that the chemical and transport effects of H2, CO and CH4 are the main factors enhancing NH3 combustion, which rising with the increasing initial temperature and decreasing ammonia blending ratio. Among the four reactants, H2 is consumed first, followed by CH4 and NH3, with CO reacting last. By modifying the Metghalchi-Kech power law equation, it was found that a clear linear relationship exists between LBV and the sum of the maximum mole fractions of O, H, OH, and NH2 radicals.

Research on the Effect of Static Pressure on the Rheological Properties of Waxy Crude Oil

In this paper, with the application of a MARS 60 high-pressure rheometer, experimental tests are conducted on Shengli crude oil to test its gel point, viscosity and thixotropy under different static pressures. Consequently, the effect of static pressure on the rheological parameters of waxy crude oil is revealed. It is proven that with the increase in the static pressure, the gel point of Shengli crude oil increases linearly, and the viscosity also gradually increases. The power law equation is employed to describe the relationship between the apparent viscosity and shear rate of Shengli crude oil under different static pressures. With the increase in the static pressure, the consistency coefficient (K) increases linearly, and the rheological index (n) decreases linearly. The relationship between the viscosity of Shengli crude oil and the static pressure and shear rate can be obtained. The Cross thixotropic model is used to describe the thixotropic curve of Shengli crude oil under different static pressures. With the increase in the static pressure, the thixotropic coefficient of consistency (ΔK) and the structure fracture constant (b) increase linearly. This is because a high pressure results in high structure strength and strong non-Newton rheological behavior in gelled crude oil and also causes remarkable structure fracture in crude oil. The results in this paper can provide an important theoretical basis for crude oil production and transportation.

Explore the fascinating realm of comparing metal melting curves by applying the equation of state and Lindemann's law

Our research, which is not just theoretical but also has practical implications, is a comprehensive study that aims to find the equation of state needed to calculate the pressure-dependent melting curves of metals. We have introduced a unique model for the melting curve, utilizing equations of state such as those proposed by Srivastava-Pandey and Kholiya. This model has been compared with Lindemann's model and available experimental data. It establishes the relationship between pressure, bulk modulus, pressure derivative of bulk modulus, and volume compression. Our findings show that a significant increase in melting temperature is directly linked to a substantial rise in bulk modulus and a gradual decrease in the first-order pressure derivative of bulk modulus. This study provides insights into understanding the effect of pressure on melting temperature. The present study finds that the equation of state of Srivastava-Pandey is more suitable for describing the melting temperature of metals, which could have significant implications for material science and engineering.

Natural mechanism of superexcellent vibration isolation of the chicken neck

No matter how the chicken's body shakes, its head can always remain relatively motionless, leading to the intuitive impression that the S-configuration of the chicken neck possesses an unparalleled vibration isolation capability. However, this viewpoint has not been rigorously substantiated. To unravel the vibration isolation mechanism inherent in the chicken neck, this study introduces a multi-modular S-configurational model inspired by its biological structure. Utilizing Newton's law and Lagrange's equations, both the static and dynamic models for the S-configurational model are formulated. Furthermore, we incorporate actuators into the model and develop a bionic attitude control method. Surprisingly, numerical simulations reveal that the S-configuration of the chicken neck does not exhibit any passive vibration isolation function, challenging the intuitive impression. Instead, the motionless of a chicken head results from active control implemented by the corresponding chicken neck. This study may contribute to a better understanding of the vibration attenuation function of the neck of birds.

Developing Countries’ Deadlock: What Does the Thirlwall's Law Offer Us?

This study aims to discuss potential alternatives for economic development in developing countries, with contributions from the theoretical background of Thirlwall's law. Developing countries' foreign trade constraints will be highlighted, followed by a comparison of Türkiye's past growth performance with results obtained from Thirlwall’s Law equations using balance of payments data. Türkiye's actual growth rates closely resemble the growth forecast of Thirlwall’s model, which indicates that post-Keynesian approaches are worth considering to alter the current situation. While providing a perfect solution that could reverse everything for developing countries may be a distant goal, this study aspires to foster a mindset capable of changing the course of events.

DiffSim: a user-friendly tool for precise magmatic timescale determination and error propagation via major element diffusion chronometry in magmatic phases

Diffusion chronometry is a technique gaining interest in the scientific community related to volcanology and petrology; however, modelling can be challenging for non-expert users. Here, we present DiffSim, a user-friendly standalone freeware that allows users to calculate magmatic timescales simulating 1D diffusion of major elements in olivine, orthopyroxene, titanomagnetite, and melt (inclusions). The freeware works solving the Fick’s second law equation (for both Cartesian and spherical polar coordinates, depending on the phase) using finite differences through the Crank-Nicolson method. Users must specify the initial composition vs. distance profile, the time resolution, and the intensive conditions (such as temperature, pressure, and oxygen fugacity). For orthorhombic phases, such as olivine and orthopyroxene, users must also specify the plunge and the trend of the (001)-axis and the angle traverse of the 2D section being studied. The best-fitting profile, comparing the natural (measured) and the modelled (calculated) profiles, is obtained using the least-squares fitting method in accordance with the total time specified by the user for performing the diffusion modelling. To determine the uncertainties of the timescale calculation, DiffSim propagates errors based on the uncertainties associated with each intensive condition and the experimental diffusivity measurements. DiffSim is available as executable freeware, allowing researchers and students to use diffusion chronometry to elucidate information about crustal processes with ease and precision.

FRESH-based 3D bioprinting of complex biological geometries using chitosan bioink

Traditional three-dimensional (3D) bioprinting has always been associated with the challenge of print fidelity of complex geometries due to the gel-like nature of the bioinks. Embedded 3D bioprinting has emerged as a potential solution to print complex geometries using proteins and polysaccharides-based bioinks. This study demonstrated the Freeform Reversible Embedding of Suspended Hydrogels (FRESH) 3D bioprinting method of chitosan bioink to 3D bioprint complex geometries. 4.5% chitosan was dissolved in an alkali solvent to prepare the bioink. Rheological evaluation of the bioink described its shear-thinning nature. The power law equation was fitted to the shear rate-viscosity plot. The flow index value was found to be less than 1, categorizing the material as pseudo-plastic. The chitosan bioink was extruded into another medium, a thermo-responsive 4.5% gelatin hydrogel. This hydrogel supports the growing print structures while printing. After this, the 3D bioprinted structure was crosslinked with hot water to stabilize the structure. Using this method, we have 3D bioprinted complex biological structures like the human tri-leaflet heart valve, a section of a human right coronary arterial tree, a scale-down outer structure of the human kidney, and a human ear. Additionally, we have shown the mechanical tunability and suturability of the 3D bioprinted structures. This study demonstrates the capability of the chitosan bioink and FRESH method for 3D bioprinting of complex biological models for biomedical applications.

Design Constant Head Permeability Meter Digital: A Project-Based Learning Media

The permeability coefficient value is one of the most important parameters in soil mechanics. Quick, simple, and digital direct soil permeability tests in the field are needed to obtain data representing conditions. This research aims to create a portable soil permeability test tool based on microcontroller automation used as a project-based learning for Transportation Cadets peculiarly Palembang Aviation Polytechnic Cadets for new experiences of new learning circumstances. This research method based on the principle of permeability testing using the constant-head method by analyzing the requirements quantitatively. This principle uses water change level parameters, which are used to test the infiltration rate in sample soil. Furthermore, measurements of changes in water level are used by water leveling sensors and processed using Arduino Uno based on fuzzy logic with access to results via the web, tool design, and simulation using SIMULINK software. The results of designing a digital measuring instrument for permeability using the constant head method have been validated for its schematic circuit using SIMULINK and can work without error. In conclusion, a model based on Darcy's Law equation and constant head to find the permeability coefficient can be generated, which can then be a prototype of the tool. It concluded the design of constant head permeability meter digital is useful as project-based leaning media for the Palembang aviation polytechnic. Furthermore, the equipment design will be the first digital measuring tool for permeability coefficient using the constant head method. The design has advantage to measure the soil permeability coefficient at the airport in the fastest way.

Molecular Modelling Comparisons, Optical and Band Gap Characterisation of 4-Sulfocalix[4]arene Thin Film

The advantageous property of water-soluble calixarenes is their ability to form stable complexes with inorganic guest molecules. Due to these attributes, their application in areas including molecular recognition, sensing, and supramolecular chemistry is extraordinarily alluring. The 4-sulfocalix[4]arene (SC[4]) is a water-soluble molecule and a derivative of the calixarene family that has both aromatic rings and sulfonate groups. The thin films were prepared using a spin-coating technique and characterised by Ultraviolet-Visible Spectroscopy (UV-Vis). By employing the Corey-Pauling-Koltun (CPK) model in conjunction with density functional theory (DFT), the height and diameter of SC[4] were precisely determined by devotedly representing its molecular shape and size. Then, the calixarene thin film’s optical properties and light absorption by the thin film were determined using the absorbance graph and Beer-Lambert law equation. The band gap energy of the thin film was determined to be equal to 4.44 eV through the Tauc-plot method. These results substantiate the integration of CPK models validated using DFT for measuring the size of SC[4] molecules and characterising the thin film’s optical characteristics. In a nutshell, the implementation of the CPK models was validated with DFT to determine the height and diameter of the SC[4] and the optical characterisation of its thin film was thoroughly determined in this study. The results obtained from this study are not only essential for understanding the properties of SC [4] but also inspire further research for multiple applications such as molecular recognition, adsorption and supramolecular chemistry.

A reality-augmented adaptive physics informed machine learning method for efficient heat transfer prediction in laser melting

Physics informed neural network (PINN) method is proposed to alleviate problems in many science and engineering scenarios when data-collection is difficult, or traditional numerical calculations are lack of convenience because more time-consuming numerical calculations are required whenever one or more parameters of the process is changed. However, for advanced manufacturing processes like laser melting (LM), a basis of laser metal additive manufacturing, involve many complex physical phenomena (e.g. melting, convection, solidification, vaporization and interface evolution), the full equations of which are too complex to be solved by current PINN. This paper proposes a reality-augmented adaptive physics informed machine learning (RAA-PIML) method to meet the objectives of precise and fast predictive LM. It applies adaptive function, integrating heat transfer law and boundary condition equations to loss function, which has fast convergence and strong physics-based constraints. The reality-augmented data are acquired by few experiments and an accurate 3D heat transfer model covering turbulence. The conducted experimental results demonstrate that the developed solution exhibits higher efficiency than simulation, and superior performance than state-of-the-art methods, which shows outstanding potential in industry applications.