EHD instability of a cylindrical interface separating two couple-stress fluids.

This article is an attempt at examining the axi-symmetric and asymmetric streaming flows described by the CSF framework. A liquid that has microfibers implanted in it, like a fiber-reinforced composite substance, is so-called CSF. It is a system that consists of an endless vertical cylindrical interface that separates the two CSF structure. The CSFs are increasingly growing significant in modern manufacturing and technology, necessitating greater research into these fluids. An axial EF acts over the cylindrical contact in addition to the influence of CSF. The VPT is employed for the sake of convenience to minimize mathematical complexity. Combining the elementary linear equations of motion and the proper linear related BCs is the major procedure of the linear technique. A collection of physically dimensionless numbers is produced using a non-dimensional process. Subsequently, the requirements for hypothetical linear stability are developed. With the aid of the Gaster's theorem, the MS is applied in computing the dispersion relationships. After carefully examining a variety of effects on the stability investigation of the system at issue, it has been shown that the system is more unstable when a porous material is present than it would be without one. The resulting axisymmetric disturbance situation is more unstable. The linear techniques are depicted throughout a number of graphs.

Different controllers for suppressing oscillations of a hybrid oscillator via non-perturbative analysis.

To arrive at an equivalent linear differential equation, the non-perturbative approach (NPA) is established. The corresponding linear equation is employed for performing the structural analysis. A numerical computation demonstrates a high consistency with the precise frequency. The correlation with the numerical solution explains the reasonableness of the obtained solutions. For additional nonlinear kinds of oscillation, the methodology gives an exact simulation. The stable construction of the prototype is shown in a series of diagrams. Positive position feedback (PPF), integral resonant control (IRC), nonlinear integral positive position feedback (NIPPF), and negative derivative feedback (NDF) are proposed to get rid of the damaging vibration in the system. It is found that the NDF control is more efficient than other controllers for vibration suppression. The theoretical methodology is applied by using the averaging method for getting a perturbed solution. The stability and influence of various parameters of the structure are established at main and 1:1 internal resonance, which is presented as one of the worst resonance cases. Association concerning mathematical solution and computational simulation is achieved.

Ensemble meta machine learning for predicting the adsorption of anionic and cationic dyes from aqueous solutions using Polymer/graphene/clay/MgFeAl-LTH nanocomposite.

Adsorption is one of the most promising wastewater treatment methods due to its simplicity and efficacy at ambient temperature and pressure. However, the technical and economic feasibility of this process largely depends on the performance of the utilized adsorbents. In this study, a promising adsorbent made of polyethyleneimine, graphene oxide (GO), bentonite, and MgFeAl-layered triple hydroxide (MgFeAl-LTH) has been synthesized and characterized. The results revealed that the synthesized nanocomposite (abbreviated as PGB-LTH) possesses good porosity and crystallinity. The adsorption performance of the PGB-LTH nanocomposite towards two harmful water pollutants (i.e., methyl orange (MO) and crystal violet (CV)) was investigated, and the results revealed that the nanocomposite outperforms its parental materials (i.e., GO, bentonite, and MgFeAl-LTH). The maximum adsorption capacity (qmax) of MO and CV onto the nanocomposite could reach 1666.7 and 1250.0 mg/g, respectively, as predicted using the Langmuir adsorption isotherm. Additionally, the PGB-LTH nanocomposite is highly reusable with an insignificant decline in performance upon repetitive use. In terms of thermodynamics, MO adsorption onto the nanocomposite is exothermic while CV adsorption is endothermic despite that both dyes adsorb spontaneously as revealed by the negative values of the Gibbs free energy change at all the examined temperatures. The generated adsorption data were utilized for constructing and assessing ensemble meta-machine learning techniques aimed at cost-effective simulation and prediction of the proposed adsorption method. Bagging and boosting methods were developed and evaluated intensively using the obtained adsorption data. The Extra Trees model achieved promising results as evidenced by the high correlation coefficient of 99% as well as low computed RMSE and MAE errors of 11.42 and 5.11, respectively, during the testing phase. These results demonstrate the model strong capability to effectively simulate and predict the adsorption process in question.

Studying highly nonlinear oscillators using the non-perturbative methodology.

Due to the growing concentration in the field of the nonlinear oscillators (NOSs), the present study aims to use the general He's frequency formula (HFF) to examine the analytical representations for particular kinds of strong NOSs. Three real-world examples are demonstrated by a variety of engineering and scientific disciplines. The new approach is evidently simple and requires less computation than the other perturbation techniques used in this field. The new methodology that is termed as the non-perturbative methodology (NPM) refers to this innovatory strategy, which merely transforms the nonlinear ordinary differential equation (ODE) into a linear one. The method yields a new frequency that is equivalent to the linear ODE as well as a new damping term that may be produced. A thorough explanation of the NPM is offered for the reader's convenience. A numerical comparison utilizing the Mathematical Software (MS) is used to verify the theoretical results. The precise numeric and theoretical solutions exhibited excellent consistency. As is commonly recognized, when the restoration forces are in effect, all traditional perturbation procedures employ Taylor expansion to expand these forces and then reduce the complexity of the specified problem. This susceptibility no longer exists in the presence of the non-perturbative solution (NPS). Additionally, with the NPM, which was not achievable with older conventional approaches, one can scrutinize examining the problem's stability. The NPS is therefore a more reliable source when examining approximations of solutions for severe NOSs. In fact, the above two reasons create the novelty of the present approach. The NPS is also readily transferable for additional nonlinear issues, making it a useful tool in the fields of applied science and engineering, especially in the topic of the dynamical systems.

The influence of energy and temperature distributions on EHD destabilization of an Oldroyd-B liquid jet.

This work examines the impact of an unchanged longitudinal electric field and the ambient gas on the EHD instability of an Oldroyd-B fluid in a vertical cylinder, where the system is immersed in permeable media. In order to explore the possible subject uses in thermo-fluid systems, numerous experimental and theoretical types of research on the subject are conducted. The main factors influencing the dispersion and stability configurations are represented by the energy and concentration equations. The linear Boussinesq approximating framework is recommended for further convenience. A huge growth in numerous physical and technical implications is what motivated this study. Using the standard normal modes of examination, the characteristics of velocity fields, temperature, and concentration are analyzed. The conventional stability results in a non-dimensional convoluted transcendental dispersion connection between the non-dimensional growth rate and all other physical parameters. The Maranogoni phenomenon, in which temperature and concentration distributions affect surface tension, has been addressed. It is observed that the intense electric field, the Prandtl numeral, the Lewis numeral, and the Lewis numeral velocity ratio have a stabilizing influence. As opposed to the Weber numeral, the Ohnesorge numeral, and the density ratio have a destabilizing influence.

Numerical analysis for tangent-hyperbolic micropolar nanofluid flow over an extending layer through a permeable medium.

The principal purpose of the current investigation is to indicate the behavior of the tangent-hyperbolic micropolar nanofluid border sheet across an extending layer through a permeable medium. The model is influenced by a normal uniform magnetic field. Temperature and nanoparticle mass transmission is considered. Ohmic dissipation, heat resource, thermal radiation, and chemical impacts are also included. The results of the current work have applicable importance regarding boundary layers and stretching sheet issues like rotating metals, rubber sheets, glass fibers, and extruding polymer sheets. The innovation of the current work arises from merging the tangent-hyperbolic and micropolar fluids with nanoparticle dispersal which adds a new trend to those applications. Applying appropriate similarity transformations, the fundamental partial differential equations concerning speed, microrotation, heat, and nanoparticle concentration distributions are converted into ordinary differential equations, depending on several non-dimensional physical parameters. The fundamental equations are analyzed by using the Rung-Kutta with the Shooting technique, where the findings are represented in graphic and tabular forms. It is noticed that heat transmission improves through most parameters that appear in this work, except for the Prandtl number and the stretching parameter which play opposite dual roles in tin heat diffusion. Such an outcome can be useful in many applications that require simultaneous improvement of heat within the flow. A comparison of some values of friction with previous scientific studies is developed to validate the current mathematical model.

Dynamical system of a time-delayed ϕ6-Van der Pol oscillator: a non-perturbative approach.

A remarkable example of how to quantitatively explain the nonlinear performance of many phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current paper examines the stability analysis of the dynamics of ϕ6-Van der Pol oscillator (PHI6) exposed to exterior excitation in light of its motivated applications in science and engineering. The emphasis in many examinations has shifted to time-delayed technology, yet the topic of this study is still quite significant. A non-perturbative technique is employed to obtain some improvement and preparation for the system under examination. This new methodology yields an equivalent linear differential equation to the exciting nonlinear one. Applying a numerical approach, the analytical solution is validated by this approach. This novel approach seems to be impressive and promising and can be employed in various classes of nonlinear dynamical systems. In various graphs, the time histories of the obtained results, their varied zones of stability, and their polar representations are shown for a range of natural frequencies and other influencing factor values. Concerning the approximate solution, in the case of the presence/absence of time delay, the numerical approach shows excellent accuracy. It is found that as damping and natural frequency parameters increase, the solution approaches stability more quickly. Additionally, the phase plane is more positively impacted by the initial amplitude, external force, damping, and natural frequency characteristics than the other parameters. To demonstrate how the initial amplitude, natural frequency, and cubic nonlinear factors directly affect the periodicity of the resulting solution, many polar forms of the corresponding equation have been displayed. Furthermore, the stable configuration of the analogous equation is shown in the absence of the stimulated force.

Nonlinear stability of two dusty magnetic liquids surrounded via a cylindrical surface: impact of mass and heat spread.

The current article examines a nonlinear axisymmetric streaming flow obeying the Rivlin-Ericksen viscoelastic model and overloaded by suspended dust particles. The fluids are separated by an infinite vertical cylindrical interface. A uniform axial magnetic field as well as mass and heat transmission (MHT) act everywhere the cylindrical flows. For the sake of simplicity, the viscous potential theory (VPT) is adopted to ease the analysis. The study finds its significance in wastewater treatment, petroleum transport as well as various practical engineering applications. The methodology of the nonlinear approach is conditional primarily on utilizing the linear fundamental equations of motion along with the appropriate nonlinear applicable boundary conditions (BCs). A dimensionless procedure reveals a group of physical dimensionless numerals. The linear stability requirements are estimated by means of the Routh-Hurwitz statement. The application of Taylor's theory with the multiple time scales provides a Ginzburg-Landau equation, which regulates the nonlinear stability criterion. Therefore, the theoretical nonlinear stability standards are determined. A collection of graphs is drawn throughout the linear as well as the nonlinear approaches. In light of the Homotopy perturbation method (HPM), an estimated uniform solution to the surface displacement is anticipated. This solution is verified by means of a numerical approach. The influence of different natural factors on the stability configuration is addressed. When the density number of the suspended inner dust particles is less than the density number of the suspended outer dust particles, and vice versa, it is found that the structure is reflected to be stable. Furthermore, as the pure outer viscosity of the liquid increases, the stable range contracts, this means that this parameter has a destabilizing effect. Additionally, the magnetic field and the transfer of heat don't affect the nature of viscoelasticity.

Dynamical analysis of an inverted pendulum with positive position feedback controller approximate uniform solution.

The inverted pendulum is controlled in this article by using the nonlinear control theory. From classical analytical mechanics, its substructure equation of motion is derived. Because of the inclusion of the restoring forces, the Taylor expansion is employed to facilitate the analysis. An estimated satisfactory periodic solution is obtained with the aid of the modified Homotopy perturbation method. A numerical technique based on the fourth-order Runge-Kutta method is employed to justify the previous solution. On the other hand, a positive position feedback control is developed to dampen the vibrations of an IP system subjected to multi-excitation forces. The multiple time scale perturbation technique of the second order is introduced as a mathematical method to solve a two-degree-of-freedom system that simulates the IP with the PPF at primary and 1:1 internal resonance. The stability of these solutions is checked with the aid of the Routh-Hurwitz criterion. A set of graphs, based on the frequency response equations resulting from the MSPT method, is incorporated. Additionally, a numerical simulation is set up with RK-4 to confirm the overall controlled performance of the studied model. The quality of the solution is confirmed by the match between the approximate solution and the numerical simulation. Numerous other nonlinear systems can be controlled using the provided control method. Illustrations are offered that pertain to implications in design and pedagogy. The linearized stability of IP near the fixed points as well as the phase portraits is depicted for the autonomous and non-autonomous cases. Because of the static stability of the IP, it is found that its instability can be suppressed by the increase of both the generalized force as well as the torsional constant stiffness of the spring. Additionally, the presence of the magnetic field enhances the stability of IP.

Dynamical system of a time-delayed of rigid rocking rod: analytical approximate solution.

The stability analysis of a rocking rigid rod is investigated in this paper using a time-delayed square position and velocity. The time delay is an additional safety against the nonlinearly vibrating system under consideration. Because time-delayed technologies have lately been the core of several investigations, the subject of this inquiry is extremely relevant. The Homotopy perturbation method (HPM) is modified to produce a more precise approximate outcome. Therefore, the novelty of the exciting paper arises from the coupling of the time delay and its correlation with the modified HPM. A comparison with the fourth-order Runge-Kutta (RK4) technique is employed to evaluate the precision between the analytical as well as the numerical solutions. The study allows for a comprehensive examination of the recognition of the outcome of the realistic approximation analytical methodology. For different amounts of the physical frequency and time delay factors, the time histories of the found solutions are depicted in various plots. These graphs are discussed in the context of the shown curves according to the relevant parameter values. The organized nonlinear prototype approach is examined by the multiple-time scale method up to the first approximation. The obtained results have periodic behavior and a stable manner. The current study makes it possible to carefully examine the findings arrived at by employing the analytical technique of practicable estimation. Additionally, the time delay performs as extra protection as opposed to the system potential for nonlinear oscillation.

Dynamical analysis of a damped harmonic forced duffing oscillator with time delay.

This paper is concerned with a time-delayed controller of a damped nonlinear excited Duffing oscillator (DO). Since time-delayed techniques have recently been the focus of numerous studies, the topic of this investigation is quite contemporary. Therefore, time delays of position and velocity are utilized to reduce the nonlinear oscillation of the model under consideration. A much supplementary precise approximate solution is achieved using an advanced Homotopy perturbation method (HPM). The temporal variation of this solution is graphed for different amounts of the employed factors. The organization of the model is verified through a comparison between the plots of the estimated solution and the numerical one which is obtained utilizing the fourth order Runge-Kutta technique (RK4). The outcomes show that the improved HPM is appropriate for a variety of damped nonlinear oscillators since it minimizes the error of the solution while increasing the validation variety. Furthermore, it presents a potential model that deals with a diversity of nonlinear problems. The multiple scales homotopy technique is used to achieve an estimated formula for the suggested time-delayed structure. The controlling nonlinear algebraic equation for the amplitude oscillation at the steady state is gained. The effectiveness of the proposed controller, the time delays impact, controller gains, and feedback gains have been investigated. The realized outcomes show that the controller performance is influenced by the total of the product of the control and feedback gains, in addition to the time delays in the control loop. The analytical and numerical calculations reveal that for certain amounts of the control and feedback signal improvement, the suggested controller could completely reduce the system vibrations. The obtained outcomes are considered novel, in which the used methods are applied on the DO with time-delay. The increase of the time delay parameter leads to a stable case for the DO, which is in harmony with the influence of this parameter. This drawn curves show that the system reaches a stable fixed point which assert the presented discussion.

EHD stability of a cylindrical boundary separating double Reiner-Rivlin fluids.

The major aim of this work is to achieve a mathematical technique to scrutinize the nonlinear instability of a vertical cylindrical boundary separation of two streaming Reiner-Rivlin liquids. The system is portrayed by an unchanged longitudinal electric strength. Furthermore, the action of mass and heat transfer (MHT) and permeable media are also considered. The problem is not only of methodological interest but also of scientific and practical interest. To shorten the mathematical analysis, Hsieh's modulation together with the viscous potential theory (VPT) is employed. The nonlinear diagram is contingent on tackling the governing linear mechanism along with the nonlinear applicable border restrictions. A non-dimensional process produces several non-dimensional physical numbers. A linear dispersion equation is attained and the stability standards are theoretically governed and numerically established. The nonlinear stability procedure reveals a Ginzburg-Landau formula. Consequently, nonlinear stability stipulations are accomplished. Furthermore, by way of the Homotopy perturbation approach, along with the expanded frequency concept, an accurate perturbed technique of surface deflection is attained theoretically and numerically. To validate the theoretical outcomes, the analytical expression is confirmed through the Rung-Kutta of the fourth order. The stable and unstable zones are signified graphically displaying the influences of several non-dimensional numbers.

Improved exosome isolation methods from non-small lung cancer cells (NC1975) and their characterization using morphological and surface protein biomarker methods.

This study has demonstrated improved methods for isolating exosomes from non-small lung cancer cells, which address the problems characterized by exosome morphological and chemical methods. To improve the isolation methods, cells from the NCI 1975 cell line were used as the source for exosomes. The isolation processes were carried out using serial isolation techniques in addition to specific preservation tools. The isolated exosomes were characterized using transmission electron microscopy (TEM), and scanning electron microscopy (SEM) was added for further assurance of the investigation results. The statistical analysis results showed that the size distributions of apoptotic vesicles (APV) 450 nm and necrotic bodies (NCB) 280 nm (extracellular vesicles) were significantly different from exosomes (P < 0.001). In contrast, the exosome size distribution was not significantly different from the published exosome sizes, as demonstrated by statistical analysis tools. This study confirmed the improved methods for isolating exosomes that make exosomes accessible for use in the diagnosis and prognosis of non-small cell lung cancer (NSCLC).

Peristaltic transport of Rabinowitsch nanofluid with moving microorganisms.

The key objective of the current examination is to examine a symmetrically peristaltic movement of microorganisms in a Rabinowitsch fluid (RF). The Boussinesq approximation, buoyancy-driven flow, where the density with gravity force term is taken as a linear function of heat and concentrations, is kept in mind. The flow moves with thermophoretic particle deposition in a horizontal tube with peristalsis. The heat distribution and volume concentration are revealed by temperature radiation and chemical reaction characteristics. The originality of the existing study arises from the importance of realizing the benefits or the threats that nanoparticles, microbes, and bacteria cause in the flow inside peristaltic tubes. The results are an attempt to understand what factors perform additional advantages and or reduce damages. The controlling nonlinear partial differential equations (PDEs) are made simpler by employing the long wavelength (LWL) and low-Reynolds numeral (LRN) approximations. These equations are subjected to a set of non-dimensional transformations that result in a collection of nonlinear ordinary differential equations (ODEs). By employing the Homotopy perturbation method (HPM), the configuration of equational analytical solutions is examined. Analytical and graphical descriptions are provided for the distributions of axial speed, heat, microbes, and nanoparticles under the influence of these physical characteristics. The important findings of the current work may help to comprehend the properties of several variations in numerous biological situations. It is found that the microorganisms condensation decays with the rise of all the operational parameters. This means that the development of all these factors benefits in shrinking the existence of harmful microbes, viruses, and bacteria in the human body's peristaltic tubes, especially in the digestive system, and large and small intestines.

Nonlinear EHD instability of two viscoelastic fluids under the influence of mass and heat transfer.

This study attempts to provide an approach to studying the nonlinear stability of a vertical cylindrical interface between two Oldroyd-B prototypes. An unchanged axial electric field influences the system, and porous medium, and the effects of heat and mass transfer (MHT) are considered. Hsieh's modulation and the viscous potential flow (VPT) are used to abbreviate the mathematical analysis. The viscoelastic Oldroyd-B model significant role in geothermal, engineering and industrial enhancement motivated us to carry out this in-depth investigation. The methodology of the nonlinear technique depends mainly on solving the linear equations of motion and applying the appropriate nonlinear boundary conditions. Numerous non-dimensional physical numbers are exposed using a non-dimensional technique. The stability conditions are theoretically achieved and numerically verified. As a limiting case, the linear dispersion equation is accomplished, and a set of stability diagrams is reachable. Together with the nonlinear stability method, a Ginzburg-Landau equation is derived. Subsequently, both theoretical and numerical methods are used to achieve the nonlinear stability criteria. Furthermore, a precise perturbed approach for surface deflection is achieved theoretically and numerically using the Homotopy perturbation method and the extended frequency conception. Along with the linear approach, it is found that the structure becomes unstable by the Laplace, Reynolds, Weber, and elasticity quantities as well as the linear MHT parameter. Furthermore, the stability zones are enhanced in the nonlinear instability approach.

ENCEPHALOPATHY TREATED AFTER SURGERY FOR GRAVES' DISEASE.

Introduction: This case report is the fourth of its type in the medical literature. It describes total thyroidectomy for recurrent relapses of Graves encephalopathy (GE) despite medical treatment. Case presentation: A 33-year-old male presented with impaired consciousness and convulsions. He had post-thyroid surgery recurrent Graves' disease with a goitre. Based on this fact, high thyroid antibodies titres and the exclusion of other causes of such neurological manifestations, he was diagnosed to have GE. This is a rare variant of "encephalopathy associated with autoimmune thyroid disease" (EAATD). Despite the administration of steroid therapy and other standard therapeutic measures, he developed five relapses within 17 months. Total thyroidectomy was advised. Unfortunately, he got another severe attack that required intensive care admission. After three days of discharging, he had urgent total thyroidectomy. The operation went well and for 18 months' follow-up he had no more attacks. However, thyroid antibodies remained high. Discussion: The report provides details on the diagnosis, standard management and the indication for thyroidectomy for GE. It describes its challenges, precautions, technique and outcomes. It reviews the extent of surgery as well as the clinical and antibody outcomes of the previous three related reports, in comparison with the current one. Conclusion: For medically uncontrolled relapse of GE, thyroidectomy consistently results in ending the attacks. It, therefore, should be put in more consideration in the treatment protocols. On the other hand, one should not depend on antibody levels as a measure of treatment success.

Heat and mass flux through a Reiner-Rivlin nanofluid flow past a spinning stretching disc: Cattaneo-Christov model.

The current work scrutinizes a non-Newtonian nanofluid free convective flow induced by a rotating stretchable disc. The examination surveys the Stefan blowing and Cattaneo-Christov mass and heat fluxes, as a precise illustrative model. The innovative aspects of the ongoing project include the analysis of the border sheet nanofluid flow near a revolving disc through thermophoresis, Reiner-Rivlin prototype features, and random nanoparticle motion. The Reiner-Rivlin non-Newtonian model is considered together with the effect of an unvarying axial magnetic strength. The constitutive formulae of a Reiner-Rivlin liquid have been reproduced in the cylindrical coordinates. Through implementing the applicable relationship transformations, the controlling partial differential equations are transferred to ordinary differential equations (ODE). This procedure yields a group of coupled nonlinear ordinary differential equations in relation to speed, heat, and nanoparticle concentration profiles that are impacted by several physical characteristics. These equations are analyzed by using the homotopy perturbation method (HPM). Due to the analytical solution given by HPM, the current work enables us to take the infinity of the layer as a parameter of the problem and discuss its variation in the obtained distributions. Consequently, a physical significant graphical visualization of the data is emphasized. The rates of mass and temperature transmission are examined to understand if any of the relevant parameters may improve these rates. Additionally, the Stefan blowing causes extra particles diffusion, which enhances heat transfer and raises the nanoparticles concentration and could be useful in some medical therapies. Furthermore, the stretching of the rotating disc is concluded, which improves the fluid heat transfer.

A Casson nanofluid flow within the conical gap between rotating surfaces of a cone and a horizontal disc.

The present study highlights the flow of an incompressible nanofluid following the non-Newtonian flow. The non-Newtonian fluid behavior is characterized by the Casson prototype. The flow occupies the conical gap between the rotating/stationary surfaces of the cone and the horizontal disc. Heat and mass transfer is also considered. The novelty of the proposed mathematical model is supplemented with the impacts of a uniform magnetic field imposed vertically upon the flow together with Ohmic dissipation and chemical reactions. The constitutive equations of the Casson fluid have been interpreted along with the cylindrical coordinates. The governing partial differential equations of momentum, energy, and concentration are converted into a set of nonlinear ordinary differential equations via appropriate similarity transformations. This scheme leads to a set of coupled nonlinear ordinary equations concerning velocity, temperature, and nanoparticles concentration distributions. These equations are analytically solved by means of the Homotopy perturbation method (HPM). The theoretical findings are presented in both graphical and tabular forms. The main objective of this study is to discuss the effects of the rotations of both cone and disc and the effects of the other parameters in the two cases of rotation alternatively. Additionally, the effect of the angle between the cone and the disk is one of our interesting points because of the importance of its effect in some engineering industry applications. The rotation parameters are found to have reduction effects on both the temperature and the radial velocity of the fluid, while they have an enhancing effect on the azimuthal velocity. The effects of other parameters with these rotations are found to be qualitatively the same as some earlier published studies. To validate the current mathematical model, a comparison with the previous scientific reports is made.

Analytical solution for the motion of a pendulum with rolling wheel: stability analysis.

The current work focuses on the motion of a simple pendulum connected to a wheel and a lightweight spring. The fundamental equation of motion is transformed into a complicated nonlinear ordinary differential equation under restricted surroundings. To achieve the approximate regular solution, the combination of the Homotopy perturbation method (HPM) and Laplace transforms is adopted in combination with the nonlinear expanded frequency. In order to verify the achievable solution, the technique of Runge-Kutta of fourth-order (RK4) is employed. The existence of the obtained solutions over the time, as well as their related phase plane plots, are graphed to display the influence of the parameters on the motion behavior. Additionally, the linearized stability analysis is validated to understand the stability in the neighborhood of the fixed points. The phase portraits near the equilibrium points are sketched.

Chitosan-dipotassium orthophosphate lyophilizate: a novel in situ thermogel carrier system of allogeneic platelet lysate growth factors.

The clinical success of platelet-rich plasma (PRP) is constrained by its limited mechanical strength, rapid disintegration by lytic enzymes, and the consequent short-term release of bioactive growth factors (GFs). Recently, attempts to formulate PRP and other hemoderivatives, such as platelet lysate (PL) have been underway. The current study aimed to formulate allogeneic freeze-dried human platelet lysate (HPL) onto lyophilized chitosan - dipotassium hydrogen orthophosphate (CS/DHO) thermo-sensitive scaffolds. A systemic approach was employed to optimize freeze-drying (FD) procedures targeting predefined critical quality attributes (CQAs). Thermal behavior, vibrational spectroscopy, morphological and moisture content analyses were used to detect possible protein destabilization during formulation and suboptimal cake properties. The effect of CS/DHO concentrations on thermo-responsiveness and release kinetics were investigated. Finally, six-months stability and cytotoxicity studies were carried out. An optimized lyophilizate was attainable with residual moisture of less than 5% and thermoresponsive to 33 °C in less than 3 min. HPL proteins were sustainedly released over five days in a pH-sensitive manner. The stability study indicated plausible physical and biochemical stability. Cell viability testing supported the cytocompatibility of the system. Finally, the lyophilizate variant of CS/DHO thermogel overcomes limited storage stability previously posed as a challenge in freshly prepared thermogels. The developed system overcomes the drawbacks of currently used PRP treatment and provides a novel GF-rich scaffold for wound repair.