Set Of Equations Research Articles

Thermo-mechanical investigation of a friction oscillator under high-frequency excitation

The frictional behavior, temperature evolution, and system dynamics in tribological systems are closely coupled. However, in many cases, at least one of the mentioned phenomena is neglected or not modeled consistently. This paper presents a model of a thermo-mechanically coupled oscillator, where the reduction of friction force due to high-frequency excitation is analyzed. The oscillator’s equation of motion, the impulse balance, and the heat equation for the thermo-mechanical continuum are evaluated so that a set of nonlinear equations describes the coupled system. Using specific mathematical procedures like Laplace-transformation and a particular transformation ansatz for integral equations, the system can be transformed into a set of ordinary differential equations, enabling efficient simulation. Based on this equation set, an averaging method is applied to eliminate the fast time scale of the mechanical oscillation due to high-frequency excitation so that only the averaged influence of the motion goes into the heat evolution. This procedure leads to concise expressions to determine the stationary state of the system, and the quantities of interest can be calculated conveniently. These equations yield parameter combinations where the friction force can be reduced due to the high-frequency excitation, even though thermal expansion is considered. However, there are also parameter regions where the excitation yields a significantly larger friction force.

Various exact solutions to the time-fractional nonlinear Schrödinger equation via the new modified Sardar sub-equation method

We aim to investigates the nonlinear Schrödinger equation including time-fractional derivative in (3+1)-dimensions by considering cubic and quantic terms The modified Sardar sub-equation method is used that lead to the discovery of a unique class of optical solutions. To transform the suggested nonlinear equation into an ordinary differential equation, we applied wave transformations, resulting in a set of nonlinear equations that offer diverse solution scenarios. The derived solutions encompass dark, wave, bright, mixed dark-bright, bell-shape, kink-shape, and singular soliton solutions. To enhance our understanding of the dynamic behavior exhibited by these solitons under varying time parameter values, visual simulations through a variety of graphs is presented. Furthermore, a comprehensive comparison is conducted, exploring a range of values for the conformable fractional order parameter. This comparison aims to highlight on the influence of fractional order variations on the solutions, contributing valuable insights into the nuanced dynamics of the system. Overall, this study serves to advance our understanding of nonlinear processes, and its potential applications in real-life phenomena. In the field of nonlinear optics, this equation can describe the propagation of optical pulses in nonlinear media. It helps in understanding the behavior of intense laser beams as they propagate through materials exhibiting nonlinear optical effects such as self-focusing, self-phase modulation, and optical solitons.

Experimental study and analysis of CO2 and SO2 absorption in various water-based nanofluids by response surface methodology

The absorption of acidic gases in the oil and gas industries is important due to their toxicity and corrosive effects. Recently, the application of nanofluids based on aqueous or organic solvents as absorbents has been examined by a variety of researchers. In this study, a single bubble column was exploited to study the effect of water-based nanofluids on the absorption processes of SO2 and CO2 using response surface methodology (RSM) based on Box-Behnken three-level experiment design. With this in mind, CO2 and SO2 are separately injected at the bottom of a bubble column filled with one of the nanofluids: Al2O3-water, SiO2-water, or ZnO-water for each experiment. Then, the rate of SO2 or CO2 absorption in the nanofluids has been elucidated. The effect of important parameters including the weight fraction of the nanoparticles (NPs) (0.01, 0.055, and 0.1 wt.%), gas–liquid contact time (150, 300, and 450 s), and the diameter of nozzle for gas injection (0.46, 0.57, and 0.68 mm) have been studied. Results revealed that the maximum molar flux of both gases was observed in the ZnO-water nanofluid, followed by the SiO2-water nanofluid. In addition, increasing the nanoparticle mass fraction and the bubble size causes the molar flux to rise. However, increasing the gas–liquid contact time causes the molar flux of the mentioned gases to decrease. Finally, a set of the accurate equations has been proposed to predict the molar flux of SO2 and CO2 in the various nanofluids assessed in this work.

Bio-Convective Flow of Micropolar Nanofluids over an Inclined Permeable Stretching Surface with Radiative Activation Energy

The focal concern of this study is to examine the behaviour of bio-convective flow featuring micropolar nanofluids over an inclined permeable stretching surface while considering the influence of radiative activation energy. This investigation addresses the complex interplay of factors such as biological activity, convective heat and mass transfer, unique attributes of micropolar fluids, the dynamics of nanofluids, and radiative effects. This analysis employed Buongiorno’s model, considering thermal radiation and activation energy on the bioconvective flow of micropolar nanofluids over an inclined stretching surface. Some suitable similarity variables were used to obtain a set of non-linear differential equations from the initial partial differential equations which were then solved numerically using the Runge-Kutta Fehberg method along with shooting technique. The effects of some physical parameters were examined on the velocity, temperature, concentration, and microorganism density profiles of the flow. The result revealed that each increase in the heat source/sink, thermal radiation, thermophoresis, and Brownian motion lead to a corresponding increase in the thermal boundary layer; activation energy increased the concentration while Peclet number and bioconvective Lewis number declined the microorganism density profile. Insights gleaned from this study can find applications in biomedical fields. Understanding the behavior of bio-convective nanofluids has implications for controlled heat transfer in medical applications like hyperthermia treatments or targeted drug delivery, thereby impacting patient care.

Three-dimensional vibration analysis of multilayered composite and functionally graded piezoelectric plates and shells

In the present paper, a coupled 3D exact electro-elastic shell model for Functionally Graded (FG) and composite piezoelectric structures is proposed. Primary variables of the electro-elastic model are the electric potential and the three displacement components. The model allows to evaluate the piezoelectric effect in terms of frequencies and vibration modes. Both closed and open circuit configurations are analyzed and compared. The 3D equilibrium equations and the 3D divergence electric displacement equation for spherical shells give the set of partial differential equations for the electro-elastic problem. The proposed model for spherical shells automatically degenerates into simpler models for plates and cylindrical shells via properly considerations on radii of curvature along in-plane directions. The orthogonal mixed curvilinear coordinates α, β and z are employed. The partial differential governing equations have constant coefficients considering fictitious layers and they are solved using the Navier harmonic form and the exponential matrix method. These features lead to an exact solution for simply-supported boundary conditions. Free vibration analyses are conducted and circular frequencies for the first three thickness vibration modes are computed. After a global assessment phase to verify the correctness of the developed model, new benchmarks are proposed: different thickness ratios and material configurations are investigated. The present work can be intended as a reference general solution for those scientists interested in the study of piezoelectric structures via 2D analytical and numerical formulations.

How hot are weakly-bound cluster ions in a blackbody field? Insights from master equation modeling

Measuring accurate energetics in mass spectrometry thermochemical and calorimetry experiments depends on detailed knowledge of the energetics of the ion populations. For example, in cases where blackbody infrared radiative dissociation (BIRD) kinetics are not in the rapid energy exchange (REX) limit, threshold dissociation energies obtained directly from experiment will be too low. When ions are not in the REX limit, the ion internal energy distributions can be modeled using a master equation (ME). The ME allows evaluation of ion internal energies over time with a set of rate equations that describe the transfer of energy from one energy state to another. Here, ME modeling that accounts for the radiative absorption and emission, and dissociation rate constants is performed to determine the energetics of two model systems, M2+(H2O)n with n = 24, 55, 96, 178 and H+(AlaGly)n with n = 4, 8, 16, 32, activated by a blackbody field at temperatures between 120 and 200 K. The hydrated cluster and oligopeptide sizes are chosen such that respective ions have comparable number of internal degrees-of-freedom. The effects of blackbody temperature and inherent properties, such as frequencies and infrared (IR) intensities, molecule size, and dissociation parameters (threshold dissociation energy, E0, and high-pressure pre-exponential factor, A∞) on the resulting ion effective temperatures, steady-state energy distributions, and BIRD kinetics are explored. ME results show that at low blackbody temperatures (<∼140 K), the steady-state internal energy distributions of the ion populations resemble those of Boltzmann distributions at the blackbody temperature. At higher blackbody temperatures (>∼140 K), rapid dissociation causes the steady-state internal energy distributions to equilibrate to lower energies where absorption and emission are competitive with dissociation. This results in ion effective temperatures that deviate from and are “colder” than the blackbody temperatures. The temperature where this transition occurs depends on the competition among absorption, emission, and dissociation, and is controlled by the dissociation parameters, vibrational frequencies, and IR intensities, as illustrated for M2+(H2O)n and H+(AlaGly)n. This work shows that, under certain conditions, the ion effective temperatures can deviate significantly from those of the blackbody field temperatures. ME modeling can be used to determine the energy content of ion complexes in mass spectrometry experiments to improve the accuracy of thermochemical and calorimetry measurements of weakly-bound clusters and for more confident assignments of conformations and structures in action spectroscopy.

B spline-based estimating equation for varying-coefficient transformation models with right censored data

This article discusses the estimating equation method for varying coefficient transformation models. The B spline technique is used to approximate the unknown functional coefficients, resulting in a parametric model. The approximated model is then given a set of estimation equations. Under some regular conditions, we demonstrate the large sample properties of the resulting estimates. Some simulation studies and a real data application are also employed to assess the performance of our proposed methodologies.

Numerical Analysis of MHD Casson Fluid Flow over a Stretching Surface with Chemical Reaction and Variable Thermal Conductivity

The motivation of the current article is to explore the Numerical analysis of MHD Casson fluid flow over a Stretching surface. Three dimensional, non-linear of an incompressible fluid flow in the presence of chemical reaction and variable thermal conductivity is considered. The mathematical model effectively describes the current flow analysis. The Governing equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with MATLAB bvp4c. The behavior of various non-dimensional parameters which are involved in the derived set of equations are described and explained in detailed through graph.

PEMPS: a phylogenetic software tool to model the evolution of metabolic pathways

BackgroundMetabolic pathways support the enzyme flux that converts input chemicals into energy and cellular building blocks. With a constant rate of input, steady-state flux is achieved when metabolite concentrations and reaction rates remain constant over time. Individual genes undergo mutation, while selection acts on higher level functions of the pathway, such as steady-state flux where applicable. Modeling the evolution of metabolic pathways through mechanistic sets of ordinary differential equations is a piece of the genotype–phenotype map model for interpreting genetic variation and inter-specific differences. Such models can generate distinct compensatory changes and adaptive changes from directional selection, indicating single nucleotide polymorphisms and fixed differences that could affect phenotype. If used for inference, this would ultimately enable detection of selection on metabolic pathways as well as inference of ancestral states for metabolic pathway function.ResultsA software tool for simulating the evolution of metabolic pathways based upon underlying biochemistry, phylogenetics, and evolutionary considerations is presented. The Python program, Phylogenetic Evolution of Metabolic Pathway Simulator (PEMPS), implements a mutation-selection framework to simulate the evolution of the pathway over a phylogeny by interfacing with COPASI to calculate the steady-state flux of the metabolic network, introducing mutations as alterations in parameter values according to a model, and calculating a fitness score and corresponding probability of fixation based on the change in steady-state flux value(s). Results from simulations are consistent with a priori expectations of fixation probabilities and systematic change in model parameters.ConclusionsThe PEMPS program simulates the evolution of a metabolic pathway with a mutation-selection modeling framework based on criteria like steady-state flux that is designed to work with SBML-formatted kinetic models, and Newick-formatted phylogenetic trees. The Python software is run on the Linux command line and is available at https://github.com/nmccloskey/PEMPS.

Smart Bioimpedance Device for the Assessment of Peripheral Muscles in Patients with COPD.

Muscle dysfunction and muscle atrophy are common complications resulting from Chronic Obstructive Pulmonary Disease (COPD). The evaluation of the peripheral muscles can be carried out through the assessment of their structural components from ultrasound images or their functional components through isometric and isotonic strength tests. This evaluation, performed mainly on the quadriceps muscle, is not only of great interest for diagnosis, prognosis and monitoring of COPD, but also for the evaluation of the benefits of therapeutic interventions. In this work, bioimpedance spectroscopy technology is proposed as a low-cost and easy-to-use alternative for the evaluation of peripheral muscles, becoming a feasible alternative to ultrasound images and strength tests for their application in routine clinical practice. For this purpose, a laboratory prototype of a bioimpedance device has been adapted to perform segmental measurements in the quadriceps region. The validation results obtained in a pseudo-randomized study in patients with COPD in a controlled clinical environment which involved 33 volunteers confirm the correlation and correspondence of the bioimpedance parameters with respect to the structural and functional parameters of the quadriceps muscle, making it possible to propose a set of prediction equations. The main contribution of this manuscript is the discovery of a linear relationship between quadriceps muscle properties and the bioimpedance Cole model parameters, reaching a correlation of 0.69 and an average error of less than 0.2 cm regarding the thickness of the quadriceps estimations from ultrasound images, and a correlation of 0.77 and an average error of 3.9 kg regarding the isometric strength of the quadriceps muscle.

Influence of oscillatory hydromagnetic field with mixed convection driven Sutterby nanofluid flow over a stretching cylinder

A nonlinear mixed convective sutterby nanofluid flow along a stretching cylinder is being studied in this article. The set of partial differential equations (PDEs) that control fluid flow is nonlinear and subject to surface constraints and similarity transformation reduces a system of PDEs to non-dimensional ordinary differential equations (ODEs), which are then solved in MATLAB Bvp5c solver which is based on the Runge–Kutta method and Shooting technique. We provide a graphic evaluation of the significant contributions made by the various physical terms to engineering measurements in the curiosity and transport domains. The study discovers that temperature distribution increases heat border viscosity but reduces thermal diffusion, whereas nonlinear convection heat improves surface heat transfer. The periodic magnetic field raises the fluid temperature while decreasing the rate of energy transfer. Furthermore, experiments have demonstrated that oscillating magnetic fields induce fluctuations with a sinusoidal pattern. Furthermore, the current study has applications in the design and manufacture of cylinder-shaped objects in various fields such as aerospace engineering, geophysics, and nuclear engineering. These include core catchers in nuclear power plant steam turbines, waxy crude oils or foodstuffs in centrifugal pumps, and deformation rates that frequently occur in practical turbomachinery and other industrial processes.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Method for remote measurement of specific conductivity and moisture of subsurface soil horizons

The aim of the research is to develop a radar method for determining the physical and chemical parameters of subsurface soil horizons, providing rapid determination of moisture and specific conductivity in the area of the plant root system. The proposed method is based on a set of Fresnel equations which describe reflection of electromagnetic waves from the interface between dielectric media in vertical and horizontal polarization of the probing signal. For the practical implementation of the method, it is proposed to use two unmanned aerial vehicles that form a bistatic radar system which irradiates the Earth's surface obliquely in order to create the Brewster's effect and increase the fraction of the radio signal reflected from subsurface horizons. The percentage of moisture and the specific conductivity of soil are calculated from the measured values of the imaginary part of the complex permittivity. The required accuracy of moisture and conductivity measurements is achieved by two-step calibration of the measuring device. The values of the moisture content and specific conductivity of soil obtained by radar at a frequency of 469 MHz are in good agreement with the results of measuring these parameters using the soil moisture meter TDR 150 Spectrum Technologies, Inc.

The state and error-feedback regulator problems for a boundary control catalytic cracking process

This research work is devoted to boundary control of a catalytic cracking reactor using state and error feedback regulators. The process mathematical model is governed by a set of partial differential equations (PDEs), for which infinite-dimensional representation and spectral properties of the system generator are employed to solve the regulation problems. The primary objective is to track a desired output reference trajectory in the presence of disturbances that are generated by a distributed parameter exosystem. Initially, a state feedback stabilizing regulator is designed to drive the process output towards the reference trajectory. The second objective is to develop a dynamic controller that employs the tracking error as input. The closed-loop plant is shown to be exponentially stable and the tracking error asymptotically approaches zero. The performances of the designed regulators are shown through numerical simulations.

Phenomenal study of microbial impact on hydrogen storage in aquifers: A coupled multiphysics modelling

Underground hydrogen storage (UHS) has been considered as an integral part of energy transition from fossil fuels to renewable sources. Porous aquifers can serve as typical sites for this purpose due to their worldwide distribution and huge storage capacity. However, the diverse microbial species that inhabit the aquifers are known to be able to catalyze in-situ biochemical reactions within the hosting rock. These reactions can normally lead to microbial consumption of hydrogen, microbial clogging of pore space and thus affect hydrogen injection and withdrawal rates as reported in the literature. So far, these phenomena have been widely reported but rarely quantified. In this study, we build a coupled hydrological-mechanical-chemical-biological (HMCB) multiphysics model to simulate these microbe-related processes during UHS in aquifers. The model consists of a complete set of partial differential equations to describe: (1) rock deformation; (2) water-hydrogen two-phase flow; (3) microbes and dissolved hydrogen transport; (4) mineral dissolution/precipitation; and (5) microbial activities involving adsorption/desorption and growth/decay. All these processes are linked together through the porosity/permeability models which consider the joint impacts of microbial clogging, mineral dissolution/precipitation and effective stress. This multiphysics model is verified against laboratory biochemical reaction data and microbial transport data. Then, the verified model is used to investigate the impacts of iron-reduction bacteria (IRB) activities on UHS in aquifers. Based on the simulation results, it can be concluded that (1) hydrogen saturation at the top surface of the aquifer is the greatest while microbial activities surrounding the injection well is stimulated the most; (2) microbial activities influence the initial few cycles of hydrogen injection and withdrawal but the impacts gradually diminish with the dissolution of Fe2O3; (3) hydrogen recovery efficiency is degraded due to the combined effects of hydrogen consumption, water production and microbial clogging with the microbial clogging impact being the most significant; and (4) effective stress impacts aquifer permeability throughout UHS operations while microbial clogging influences it in the initial few cycles. For mineral dissolution/precipitation, the impact can be neglected.

On G2 approximation of planar algebraic curves under certified error control by quintic Pythagorean-hodograph splines

The Pythagorean-Hodograph curve (PH curve) is a valuable curve type extensively utilized in computer-aided geometric design and manufacturing. This paper presents an approach to approximate a planar algebraic curve within a bounding box by employing piecewise quintic PH spline curves, while maintaining G2 smoothness of the approximating curve and preserving second-order geometric details at singularities. The bounding box encompasses all x-coordinates of key topological points, ensuring accurate representation. The paper explores the analysis of the G2 interpolation problem for quintic PH curves with invariant convexity, transforming the quest for interpolation solutions into identifying positive roots within a set of algebraic equations. Through infinitesimal order analysis, it is established that a solution necessarily exists following adequate subdivision, laying the groundwork for practical application. Finally, the paper introduces a novel algorithm that integrates prior research to construct the approximating curve while maintaining control over the desired error levels.

Thermal analysis on Ferro Casson nanofluid flow over a Riga plate with thermal radiation and non-uniform heat source/sink

Ferro hybrid nanofluids can be used in electronics and microelectronics cooling applications to reduce heat accumulation and efficiently remove surplus heat. These nanofluids aid to maintain optimum operating temperatures and reduce device overheating by enhancing the heat transfer rate. With this motivation, the aim of the present numerical analysis is to study the three-dimensional incompressible hybrid nanofluid flow over a slippery Riga surface by combining the Casson fluid model. Mathematical modeling is constructed with nanoparticles as Fe3O4 and CoFe2O4 with base fluid as water. The non-uniform heat source/sink and thermal linear radiation effects are taken into account with the Hamilton–Crosser thermal conductivity model. A system of nonlinear PDEs is produced by the proposed problem and then the relevant similarity variables are implemented to transform the set of partial differential equations and their accompanying boundary conditions into the coupled nonlinear differential equations with one independent variable. These modified ordinary differential equations (ODEs) were then successfully solved with the Runge–Kutta fourth-order method by combining via the shooting technique. With the aid of graphical representations, the effects of various influencing parameters were presented and analyzed comprehensively. Furthermore, the impacts of relevant parameters on heat transfer rates and shear stress are concisely discussed and illustrated in tabular forms. The significant findings include the enhancement of the radiation parameter increases the thermal boundary layer thickness and the thickness increases whenever surface experiences slippery conditions. The axial and transverse momentum of the fluid are controlled with the Casson parameter. An effective connection is noticed once the current numerical solutions are verified under particular conditions that were previously described.

Nambu-covariant many-body theory II: Self-consistent approximations

The theory of Self-Consistent Green’s Function (SCGF) is reformulated in an explicit Nambu-covariant fashion for applications to many-body systems at non-zero temperature in symmetry-broken phases. This is achieved by extending the Nambu-covariant formulation of perturbation theory, presented in the first part of this work, to non-perturbative schemes based on self-consistently dressed propagators and vertices. We work out in detail the self-consistent ladder approximation, motivated by a trade-off between numerical complexity and many-body phenomenology. Taking a complex general Hartree–Fock–Bogoliubov (HFB) propagator as a starting point, we also formulate and prove a sufficient condition on the stability of the HFB self-energy to ensure the convergence of the initial series of ladders at any energy. The self-consistent ladder approximation is written purely in terms of spectral functions and the resulting set of equations, when expressed in terms of Nambu tensors, are remarkably similar to those in the symmetry-conserving case. This puts the application of the self-consistent ladder approximation to symmetry-broken phases of infinite nuclear matter within reach.

A compensation method for PMSM sensorless control with parameter identification considering SMO observation error

AbstractSensorless control of permanent magnet synchronous motor (PMSM) can increase the reliability of electric actuators of more electrical aircraft. Numerical online parameter estimation method will enhance the performance for sensorless control methods based on sliding mode observer (SMO). However, numerical online parameter identification methods typically assume zero rotor position estimation error to ensure full rank of the identification equation set. This assumption actually leads to errors in parameter identification, resulting in steady‐state errors in rotor position estimation. This paper focuses on a compensation method for PMSM online parameter identification that takes into account rotor position estimation error. This method is used for sensorless control based on SMO, using model reference adaptive systems for online parameter identification, and no additional parameter adjustment required. Validation is conducted on a PMSM experimental platform with maximum load of 15kW. The experimental results of 1000 r/min steady state operation proved the effectiveness of the method, and the dynamic experiments with 5 and 15kW loads proved that the method has no significant adverse effect on the system dynamics.

Ternary hybrid nanofluid flow through an inclined shrinking sheet when soret, dufour and quadratic thermal radiation are significant: an irreversibility analysis with various shape factors

As nanofluid technology continues to evolve, the knowledge gained from studying flow over an inclined shrinking sheet can be applied to various emerging applications. These could include heat pipes for spacecraft thermal management, thermal management systems for wearable electronics, or even designing microfluidic channels for efficient desalination processes. A ternary hybrid nanofluid (Ethylene Glycol, Copper (II) oxide, Titanium dioxide, and Silicon dioxide) is the main focus of this study, which aims to theoretically analyse its behaviour through a tilted shrinking sheet in the presence of heat source, Dufour, and Soret effects. Governing equations are transformed into a set of ordinary differential equations using appropriate similarity transformations and then solved using bvp4c solver. The main findings of this study are that enhancing the value of the couple stress parameter leads to a decline in fluid velocity, and increasing the Dufour number will upsurge the temperature of the fluid. It has been noticed that the Sherwood number exhibits a decline when the Soret number increases. We find that the Nusselt number noticeably increases by 0.147404161 (spherical), 0.151277029 (brick), and 0.156726935 (cylinder) for values of the Dufour number within the range of 0 to 3.