Solution Curves Research Articles

Surface Modification of 304L Stainless Steel and Interface Engineering by HiPIMS Pre-Treatment

A clean and defect-free substrate/coating interface is required to guarantee good adhesion of coatings under service conditions. For this purpose, an etching pre-treatment using High-Power Impulse Magnetron Sputtering (HiPIMS) was performed to modify the surface of 304L stainless steel. The effect of three etching procedures on the substrate properties, such as corrosion resistance and adhesion, was investigated with unprecedented spatial resolution and spectroscopic details. Glancing angle X-ray diffraction showed modification in phase content but no neoformation after steel etching. X-ray photoelectron spectroscopy confirmed the presence of etchant species (6–7 at.%) on the extreme surface of the substrate. Transmission Electron Microscopy and Atomic Probe Tomography showed that the interface was less than a few nanometers wide. Polarization curves in a nitric acid solution at boiling temperature showed, for the first time, that the Ti+ and Zr+ etchings decreased the corrosion current density compared to the untreated original surface. Scratch-test measurements indicated better substrate/coating adhesion using HiPIMS metal ion etching. Electrochemical characterization revealed that Zr etching and thin coating improve the anti-corrosion properties of stainless steel in strong nitric acid conditions.

Species Surface Distribution and Surface Tension of Aqueous Solutions of MIBC and NaCl Using Molecular Dynamics Simulations.

Methyl isobutyl carbinol (MIBC) is a high-performance surfactant with unusual interfacial properties much appreciated in industrial applications, particularly in mineral flotation. In this study, the structure of air–liquid interfaces of aqueous solutions of MIBC-NaCl is determined by using molecular dynamics simulations employing polarizable and nonpolarizable force fields. Density profiles at the interfaces and surface tension for a wide range of MIBC concentrations reveal the key role of polarizability in determining the surface solvation of Cl− ions and the expulsion of non-polarizable Na+ ions from the interface to the liquid bulk, in agreement with spectroscopic experiments. The orientation of MIBC molecules at the water liquid–vapor interface changes as the concentration of MIBC increases, from parallel to the interface to perpendicular, leading to a well-packed monolayer. Surface tension curves of fresh water and aqueous NaCl solutions in the presence of MIBC intersect at a reproducible surfactant concentration for a wide range of salt concentrations. The simulation results for a 1 M NaCl aqueous solution with polarizable water and ions closely capture the MIBC concentration at the intercept. The increase in surface tension of the aqueous MIBC/NaCl mixture below the concentration of MIBC at the intersection seems to originate in a disturbance of the interfacial hydrogen bonding structure of the surface liquid water caused by Na+ ions acting at a distance and not by its presence on the interface.

Asymptotic analysis of hepatitis B epidemic model using Caputo Fabrizio fractional operator

AbstractA mathematical model representing the temporal dynamics of hepatitis B virus (HBV) is discussed in this research work. This is based on the asymptomatic carriers and symptomatic individuals keeping in view the characteristics of the disease. We also incorporate the vaccination parameter to vaccinate susceptible individuals. Moreover, we use fractional calculus to extend the model to its associated fractional-order. For this, we particularly use the fractional operator of the Caputo-Fabrizio type to fractionalize the proposed model. First, the model formulation has been derived in classic order and then extended to its associated fractional-order version for generalization. The model equilibria was calculated, and the basic reproductive number was found. Then we will discuss the existence with properties of the uniqueness of the proposed fractional version of the model that is under consideration. The positivity with boundedness is shown to investigate that the considered model is feasible biologically as well as mathematically. Finally, we use the Mittag–Leffler approach to visualize the model of fractional-order and to support the results carried out in the theocratical part. We also demonstrate the solution curves for different values of the fractional parameter to differentiate between integer-order and fractional-order on the disease transmission.

Pillar[6]arene: Electrochemistry and application in electrochemical (bio)sensors

Electrochemical behavior of pillar[6]arene (P[6]A) was investigated for the first time in solution and on the surface of the glassy carbon electrode covered with carbon black by cyclic voltammetry and electrochemical quartz crystal microbalance. Reversible redox peaks on voltammograms corresponded to the redox conversion of hydroquinone units of the macrocycle with no effect of intramolecular hydrogen bonds. The adsorption of the macrocycle oxidation products did not affect reversibility of the electron transfer. The P[6]A adsorption on the carbon black improved the stability of redox characteristics against those in homogeneous conditions, especially in basic media. The adsorbed P[6]A retained its ability to supramolecular interactions and showed mediator properties attractive for application in electrochemical (bio)sensors. This was proved by determination of paraquat after its accumulation on the pillar[6]arene – carbon black coating with the limit of detection of 0.5 μM. The P[6]A modified electrode was also applied as a transducer of the acetylcholinesterase biosensor. Mediated oxidation of thiocholine was amperometrically monitored at 0.25 V. The biosensor made it possible to determine berberine, a reversible inhibitor of the enzyme, and two anticholinesterase pesticides, carbofuran and malaoxon. The biosensor showed high stability of the response and low detection limits of the inhibitors (1 nM for berberine and 0.1 nM for carbofuran and malaoxon). The acetylcholinesterase biosensors were also tested on spiked samples of urine (berberine) and peanut. The recovery calculated from the calibration curve of standard analyte solutions was in the range from 86 to 113%.

On the classification and evolution of bifurcation curves for a quasilinear regularized MEMS model

The quasilinear equation −(u′(x)1+(u′(x))2)′=λ(1−u)2−λɛ2(1−u)4 with the boundary condition u(−L)=u(L)=0 governs the steady-state solutions from a regularized MEMS model. We prove that for any evolution parameters ɛ∈(0,1) and L>0, the global bifurcation curve of positive solutions is strictly increasing or ⊃-like shaped or S-like shaped in the (λ,‖u‖∞)-plane. The bifurcation curves present a variety of shapes and structures, significantly different from those in non-regularized case (i.e., ɛ=0) and in the simplified semilinear case. The main tools are some new time-map techniques, the total positivity theory, and Sturm’s Theorem.

A photo-sensitive BiVO4@Bi2O3@g-C3N4 sensor for the detection of dopamine

Dopamine (DA) plays an important biological role in cardiovascular, renal, hormone, central nervous systems and human metabolism. Photo-sensitive sensors studies are gained great importance in recent years due to some problems in enzyme-based sensors. In this study, photo-sensitive BiVO4@Bi2O3@g-C3N4 based sensor is fabricated for DA determination. The semiconductors use in this sensor system have important functions; g-C3N4 is a photosensitive material, δ-Bi2O3 is a stable electrode responsible for intermediate contact, and BiVO4 is a good electron conduction material due to its stable structure. DA is analyzed by BiVO4@Bi2O3@g-C3N4 photo-sensitive sensor in 0.1 M PBS medium at solutions with different concentrations. In this study, for the first time, a calibration curve is constructed from Tafel curves of solutions of different concentrations. The DA sensor is worked in a linear range of 25–750 µM. In addition, in this developed sensor, limit of detection (LOD), limit of quantification (LOQ) and sensitivity values are 0.046, 0.154 µM and 0.011 μA µM−1 cm−2, respectively. Our strategy opens a new pathway to determination of some neurotransmitter via photo-sensitive materials.

Solution of 1<sup>st</sup> Order Stiff Ordinary Differential Equations Using Feed Forward Neural Network and Bayesian Regularization Algorithm

A stiff equation is a differential equation for which certain numerical methods are not stable, unless the step length is taken to be extraordinarily small. The stiff differential equation includes few terms that could result in speedy variation in the solution. When integrating a differential equation numerically, the requisite step length should be incredibly small. In the solution curve, much variation can be observed where the solution curve straightens out to approach a line with slope almost zero. The phenomenon of stiffness is observed when the step-size is unacceptably small in a region where the solution curve is very smooth. A lot of work on solving the stiff ordinary differential equations (ODEs) have been done by researchers with numbers of numerical methods that currently exist. Extensive research has been done to unveil the comparison between their rate of convergence, number of computations, accuracy, and capability to solve certain type of test problems. In the present work, an advanced Feed Forward Neural Network (FFNN) and Bayesian regularization algorithm-based method is implemented to solve first order stiff ordinary differential equations and system of ordinary differential equations. Using proposed method, the problems are solved for various time steps and comparisons are made with available analytical solutions and other existing methods. A problem is simulated using proposed FFNN model and accuracy has been acquired with less calculation efforts and time. The outcome of the work is showing good result to use artificial neural network methods to solve various types of stiff differential equations in near future.

The General Solution for Affine Control Systems on Lie Groups

The purpose of this paper is to present explicitly the solution curve for commutative affine control systems on Lie groups under the assumption that the automorphisms associated with the linear vector fields commutes. If we assume that the derivations associated with the linear vector fields of the system are inner, we obtain a simpler solution and we show some results of controllability. To finish, we work with conjugation by homomorphism of Lie groups between affine systems.

A continuation method for computing the multilinear PageRank

AbstractThe multilinear PageRank model [Gleich et al., SIAM J Matrix Anal Appl, 2015;36(4):1507–41] is a tensor‐based generalization of the PageRank model. Its computation requires solving a system of polynomial equations that contains a parameter . For , this computation remains a challenging problem, especially since the solution may be nonunique. Extrapolation strategies that start from smaller values of and “follow” the solution by slowly increasing this parameter have been suggested; however, there are known cases where these strategies fail, because a globally continuous solution curve cannot be defined as a function of . In this article, we improve on this idea, by employing a predictor‐corrector continuation algorithm based on a more general representation of the solutions as a curve in . We prove several global properties of this curve that ensure the good behavior of the algorithm, and we show in our numerical experiments that this method is significantly more reliable than the existing alternatives.

Nucleation of creases and folds in hyperelastic solids is not a local bifurcation

We consider creases and folds in compressed hyperelastic solids from the point of view of bifurcation theory. They refer to highly localized surface deformations that occur at compressive loads significantly below the value of the well-known Biot instability. Much work from the literature attempts to make the case that this phenomenon corresponds to a “local bifurcation” distinct from the Biot instability. A local bifurcation is a path of equilibrium solutions emanating from a (bifurcation) point on the trivial solution branch that exists in all sufficiently small neighborhoods of that bifurcation point. The inference is usually made by first introducing a small surface imperfection; a solution curve is then obtained that is seemingly close to a perfect bifurcation diagram. However, imperfection theory is valid only in some sufficiently small neighborhood of a bifurcation point. Thus, in the absence of an equilibrium path connecting these solutions to the trivial one, there is no justification for concluding that creasing and folding are local bifurcations of the perfect system.In this work, we directly address the nucleation of these solutions in the perfect, imperfection-free case. We demonstrate that surface instabilities in functionally graded and bilayer elastic halfspaces, corresponding to local bifurcations from the homogeneous state, are necessarily smooth and oscillatory; creases/folds eventually do develop along the global bifurcating solution branches, albeit “far” from the trivial solution, as evidenced by the corresponding bifurcation diagrams. In addition, we find that their stable realization occurs at load levels well below that of the initial surface instability. Moreover, we obtain such results for the perfect homogeneous halfspace, by switching the continuation parameter from macroscopic lateral strain to the film-to-substrate shear modulus ratio. When this ratio reaches unity, we obtain the desired localized deformation solution, avoiding the need for analysis near the highly degenerate homogeneous state at the Biot instability.

Investigating matrix interference in the pharmacopeial limit test for aluminum in citric acid: a re-examination, for revision of the method

In many pharmacopoeias, the limit test used for determining the level of aluminum in citric acid labeled for use in the manufacture of dialysate, is based on solvent extraction using 8-hydroxyquinoline and measurement of fluorescence. However, the fluorescence intensity (F.I.) readout from the extract of citric acid samples has been found to be highly dubious, showing low value, and even lower than that of a blank solution. The aim of this work therefore was to examine what effects the matrix has on the test. The comparison of the two standard curves of aluminum solutions in water, against those prepared in citric acid solutions revealed that they differed greatly in terms of slope and y-intercept. In addition, the F.I. values on the plot of the citric acid solution were much lower than that prepared in the water. In another experiment, a decrease in the F.I. of aluminum solution was clearly seen when the co-existing concentration of citric acid was increased. The results inferred that citric acid interfered with the test due to its acidity and metal-chelating capabilities. Based on this evidence, the pharmacopeial limit test for aluminum in citric acid should be revised; otherwise, it could yield results that underestimate aluminum levels and lead to inaccurate conclusions

Geodesic Rays of the N-Body Problem

For the Newtonian N-body problem, we study the Jacobi-Maupertuis metric of the nonnegative energy levels. We show that the geodesic rays are expansive, that is to say, all the distances between the bodies must be divergent functions. More precisely, we prove that the evolution of such motions asymptotically decomposes into free particles and subsystems in completely parabolic expansion. The theorem applies in particular to the maximal characteristic curves of any given global viscosity solution of the stationary Hamilton-Jacobi equation $H(x,d_xu) = h$.

Bifurcation curves of positive solutions for one-dimensional Minkowski curvature problem

<abstract><p>In this paper, we study the shape of the bifurcation curves of positive solutions for the one-dimensional Minkowski-curvature problem. By developing some new time mapping techniques, we find that the bifurcation curve is $ \subset $-shaped/monotone increasing/$ S $-like shaped on the $ (\lambda, ||u||_\infty) $ plane when the nonlinearity satisfies different assumptions. Finally, two examples are given to illustrate our result.</p></abstract>

Electrochemical performance of H+ implantation intercalate with LiCo3O4 thin film and its applications

The purpose of this research is to explore into the impacts of H+ ion implantation on Al/ LiCo3O4/ITO (MIS) thin films employing the sprayed pyrolysis method. The discharged and recharged specimens were characterized using XRD, EDAX, and SEM techniques. Using LiCo3O4 CV curves in KOH solution at various scan speeds, the electrochemical behavior was investigated. Li+ and H+ ions from a KOH solution underwent a reversible insertion into the diffusion coefficient values of LiCo3O4 particles. Increased protonic conductivity and a higher diffusion coefficient value of 3.55x10−8 cm2/S with a scan rate of 100 mV/S are the results of the intercalation of lithium with the cobalt oxide LiCo3O4 and this implantation affects the possible causes of the observed changes in the properties of lithium cobalt oxides. The spray pyrolysis method's process parameters have a major impact on the H+ implantation film's characteristics. As a result, they have been enhanced to produce high-quality LiCo3O4 films with excellent electrical conductivity and transparency.

Nonlinear Dynamics and Bifurcation Analysis of a Hinged-Clamped Beam Under Parametric and Internal Resonances

The present study examines the stability and bifurcation of axially moving hinged-clamped beams subjected to parametric excitation originating due to speed alterations. Attention is paid to the principal parametric resonance amid 3:1 internal resonance in the subcritical speed regime. The direct method of multiple scales is applied to predict the nonlinear behavior of the beam modeled in the form of the nonlinear integro-partial differential equation. A continuation algorithm is used to solve numerical examples to illustrate the stability and bifurcations of periodic solutions for the given set of system parameters. The fixed point solution is different for different modes. Three kinds of equilibrium solution curves like trivial, two-mode, and single-mode solutions are obtained from numerical computations. The first two kinds are available for both first and second modes while the third one is available for the second mode only. The introduction of material damping converts the isolated two-mode solution into an isolated closed-loop form. The system displays saddle-node and Hopf bifurcation points in both modes while super and subcritical pitchfork bifurcation points in the second mode only. Decreasing viscous damping strengthens the effect of internal resonance. The numerically simulated results are unique, interesting, and are not available in the existing literature.

A Multi-Strategy Seeker Optimization Algorithm for Optimization Constrained Engineering Problems

This paper proposes a multi-strategy seeker optimization algorithm (MSSOA) for optimization constrained engineering problems. In this paper, three strategies were adopted to improve the poor searching capability of the seeker optimization algorithm (SOA). The first strategy was triple black hole system capture to solve the local optima issue. The second and third strategies were the multi-dimensional random interference and the precocious interference to balance the exploration and exploitation processes. These three strategies are proposed to improve respectively the SOA algorithm, and compared with the three strategies to improve together the SOA algorithm for optimizing 15 benchmark functions; the way these three strategies work together is called multi-strategy; and the efficiency of the multi-strategy is illustrated the numerical optimizing results and the convergence curves, population’s positions with iterations and the search history of the benchmark functions. The proposed multi-strategy method achieved better performance in optimizing of the benchmark functions compared to other six optimization methods. The numerical and experimental results analysis were observed with respect to the optimal solution curve, the convergence curve of the fitness function, the ANOVA tests, the calculation complexity of the algorithm, the running time of the algorithm routine, the exploration and exploitation capability, the Wilcoxon’s rank-sum test, the performance profile of algorithm. The results showed that the proposed multi-strategy method was efficient in the benchmark functions. The proposed multi-strategy method also achieved better performance in optimizing of the engineering problems and provided better solutions compared to other six optimization methods.

Stability and bifurcation control analysis of a delayed fractional-order eco-epidemiological system.

Considering the factor of artificial intervention in biological control, a delayed fractional eco-epidemiological system with an extended feedback controller is proposed. By using the digestion delay as bifurcation parameter, the stability and Hopf bifurcation are investigated, and the branching conditions are given. The system undergoes Hopf bifurcation, when the parameter tau passes through the critical value. In addition, it can be pointed out that the negative feedback gain and the feedback delay could affect the bifurcation critical value of the system. Therefore, the Hopf bifurcation can also be induced by taking the feedback delay as a bifurcation parameter. Finally, by plotting the solution curve of the system, the significance of the controller to the stability of the eco-epidemiological system is verified.

Hall and ion-slip effects on MHD fluid flow in a rotating curved duct with aspect ratio 3

This study numerically investigates the fully developed two-dimensional, steady, viscous, incompressible magnetohydrodynamic fluid flow that passes through a rotating curved duct with an aspect ratio of 3. The curvature of the duct has been taken over a wide range of 0.01 ≤ δ ≤ 0.5. The governing equations are derived from the Navier–Stokes equations, and these equations are transformed into their non-dimensional form by applying usual transformations. The velocity of the flow is influenced by a pressure gradient force (namely, Dean forces) along the axial direction of the curved duct. The flow is also accelerated due to the combined action of the centrifugal and Coriolis forces. The effects of the Dean number, rotation, magnetic, Hall, and ion-slip parameters are examined on that flow. The spectral method is used as the primary tool to calculate the numerical solution, while the Chebyshev polynomial, collocation, and Newton–Raphson methods are used as supporting tools. The arc length method has also been used to calculate the results at any point of the critical zone of the solution curve. The main focal point of this paper is to investigate the effect of the magnetic parameter, Hall parameter, and ion-slip parameter on the flow characteristics in the rotational curve duct with a comparatively large aspect ratio. There are symmetric 2-, 4-, up to 12-vortex solutions that have been found for the streamlines of the secondary flow. In contrast, 1-, 2-, up to uncountable contour plots have been found for the axial flow. Specifically, asymmetric flow structures have been found for a small curvature and large Dean number.

A computational study on flow characteristics and energy distribution in a rotating coiled rectangular duct with longitudinal vortex generation

Investigation on fluid flow and energy distribution in a rotating coiled rectangular duct (CRD) with differentially heated horizontal walls has been analyzed numerically by using a spectral-based numerical scheme. The system is rotated around the vertical axis in the clockwise direction over the Taylor number (Tr) ranging from 0 to 2000 keeping the other parameters constant as aspect ratio Ar =3, curvature ratio BETA=0.5 the Dean number Dn = 1000 and the Prandtl number Pr = 7.0 (water). To reveal steady solution (SS) curves, we applied path continuation technique and obtained five asymmetric SS curves comprising with 2- to 8-pair cell. A bar diagram is also drawn to visualize, at a glance, longitudinal vortex generation on various curves of steady solutions. To explore unsteady behavior, time-progression analysis is performed and flow characteristics are precisely determined by obtaining phase space trajectory of the solutions. The transient flow demonstrates various stages of physically realizable solutions including chaotic, multi-periodic, periodic and steady-state; and it is found that the number of secondary vortices declines as Tr is increased. Convective heat transfer (CHT) is computed and the corresponding dependence on the flow stages is discussed accurately. Finally, a comparison has been made between the numerical computation and experimental investigations which shows a benchmark agreement.

A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results; however, due to the instantaneous interest rate and instantaneous volatility in the model following the Feller square root process, only a semi-closed solution can be obtained by solving PDEs. This paper presents a simplified approach to price log-return variance swaps under the CIR–Heston hybrid model. Compared with Cao’s work, an important feature of our approach is that there is no need to solve complex PDEs; a closed-form solution is obtained by applying the martingale theory and Ito^’s lemma. The closed-form solution is significant because it can achieve accurate pricing and no longer takes time to adjust parameters by numerical method. Another significant feature of this paper is that the impact of sampling frequency on pricing formula is analyzed; then the closed-form solution can be extended to an approximate formula. The price curves of the closed-form solution and the approximate solution are presented by numerical simulation. When the sampling frequency is large enough, the two curves almost coincide, which means that our approximate formula is simple and reliable.