Wave Propagations in Nonlinear Low-Pass Electrical Transmission Lines through Optical Fiber Medium

The present article discovers the new soliton wave solutions and their propagation in nonlinear low-pass electrical transmission lines (NLETLs). Based on an innovative Exp-function method, multitype soliton solutions of nonlinear fractional evolution equations of NLETLs are established. The equation is reformulated to a fractional-order derivative by using the Jumarie operator. Some new results are also presented graphically to understand the real physical importance of the studied model equation. The physical interpretation of waves is represented in the form of three-dimensional and contour graphs to visualize the underlying dynamic behavior of these solutions for particular values of the parameters. Moreover, the attained outcomes are generally new for the considered model equation, and the results show that the used method is efficient, direct, and concise which can be used in more complex phenomena.

Theoretical Analysis of Activation Energy Effect on Prandtl–Eyring Nanoliquid Flow Subject to Melting Condition

This study models the convective flow of Prandtl–Eyring nanomaterials driven by a stretched surface. The model incorporates the significant aspects of activation energy, Joule heating and chemical reaction. The thermal impulses of particles with melting condition is addressed. The system of equations is an ordinary differential equation (ODE) system and is tackled numerically by utilizing the Lobatto IIIA computational solver. The physical importance of flow controlling variables to the temperature, velocity and concentration is analyzed using graphical illustrations. The skin friction coefficient and Nusselt number are examined. The results of several scenarios, mesh-point utilization, the number of ODEs and boundary conditions evaluation are provided via tables.

An entropy optimization study of non-Darcian magnetohydrodynamic Williamson nanofluid with nonlinear thermal radiation over a stratified sheet

The assessment of the Darcy–Forchheimer flow of magnetohydrodynamic Williamson nanofluid with entropy optimization is the main purpose of this article. This study was carried out to analyze the impacts on fluid flow via a stratified plate. The impacts of viscous dissipation, chemical reaction, and Joule heating are examined in the existence of nonlinear thermal radiation. The framework of partial differential expressions is transformed into ordinary differential equations by utilizing a suitable set of similarity transformations. The obtained differential equations are analytically tackled by the homotopy analysis approach. -curves, table of convergence, and graphical outcomes are displayed and examined by using MATHEMATICA software. A distinctive parameter chart, against the profiles of temperature, velocity, and concentration with relevant discussion is portrayed for emphasizing their physical importance. Through graphical representations, the Sherwood number, the coefficient of skin friction, local Nussel1t number, and entropy generation impact are examined. This kind of study is useful in many industries like solar engineering, polymer extrusion, electronic supplies, biomedical, etc.

Quantum Features of Atom–Field Systems in the Framework of Deformed Fields

We propose a new kind of Schrödinger cat state introduced as a superposition of spin coherent states in the framework of noncommutative spaces. We analyze the nonclassical features for these noncommutative deformed states in terms of the main physical parameters. The physical importance of deformed states is that they provide a convenient description of a large set of laser systems. As an application, we develop the Jaynes–Cummings model by considering the interaction among atoms and cat state fields associated to deformed spin algebras. In this context, we show the dynamical behavior of the nonlocal correlation and nonclassical properties in these quantum systems.

Imposed pressure driven flow in peristalsis

Peristaltic transport phenomena are of great significance in biological sciences. The physiological transport of fluid takes place under the action of peristalsis generated as a pressure gradient. The peristaltic waves generate a pressure gradient which is responsible for the fluid flow in the forward direction. The further properties of this phenomena can be seen if an imposed pressure gradient is applied in addition to the one appearing due to peristaltic waves. This situation has not been discussed in the literature that needs further attention. The effects of the wavy boundaries and imposed pressure on the velocity of the flow field are analyzed. Here we impose a question: what happens if an imposed pressure gradient is also applied? This question of physical importance has not been addressed; and thus, remains the topic of this study. In previous papers of peristaltic motion, the flow generated by peristaltic waves only has been examined while in this study we will discuss the contribution of imposed pressure gradient on velocity field. The analytical results for the velocity field are obtained using the boundary perturbation method. The study shows that the impact of the wavy boundaries on the flow increases with the increase in corrugation parameter and imposed pressure.

Residual Power Series Method for Fractional Swift–Hohenberg Equation

In this paper, the approximated analytical solution for the fractional Swift–Hohenberg (S–H) equation has been investigated with the help of the residual power series method (RPSM). To ensure the applicability and efficiency of the proposed technique, we consider a non-linear fractional order Swift–Hohenberg equation in the presence and absence of dispersive terms. The effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are studied and presented through plots. The results obtained show that the proposed technique is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology.

Environmentally controlled curvature of single collagen proteins

The predominant structural protein in vertebrates is collagen, which plays a key role in extracellular matrix and connective tissue mechanics. Despite its prevalence and physical importance in biology, the mechanical properties of molecular collagen are far from established. The flexibility of its triple helix is unresolved, with descriptions from different experimental techniques ranging from flexible to semirigid. Furthermore, it is unknown how collagen type (homo-vs. heterotrimeric) and source (tissue-derived vs. recombinant) influence flexibility. Using SmarTrace, a chain tracing algorithm we devised, we performed statistical analysis of collagen conformations collected with atomic force microscopy (AFM) to determine the protein’s mechanical properties. Our results show that types I, II and III collagens – the key fibrillar varieties – exhibit molecular flexibilities that are very similar. However, collagen conformations are strongly modulated by salt, transitioning from compact to extended as KCl concentration increases, in both neutral and acidic pH. While analysis with a standard worm-like chain model suggests that the persistence length of collagen can attain almost any value within the literature range, closer inspection reveals that this modulation of collagen’s conformational behaviour is not due to changes in flexibility, but rather arises from the induction of curvature (either intrinsic or induced by interactions with the mica surface). By modifying standard polymer theory to include innate curvature, we show that collagen behaves as an equilibrated curved worm-like chain (cWLC) in two dimensions. Analysis within the cWLC model shows that collagen’s curvature depends strongly on pH and salt, while its persistence length does not. Thus, we find that triple-helical collagen is well described as semiflexible, irrespective of source, type, pH and salt environment. These results demonstrate that collagen is more flexible than its conventional description as a rigid rod, which may have implications for its cellular processing and secretion.

Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation

We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto-acoustic waves in plasma (Zhdanov, 1984) etc. In addition, there are plenty of equations of physical importance, having their origin in fiber optics, hydrodynamics, plasma physics and many other areas, which are gauge equivalent to the NLS equation or to the KP-I equation. Therefore our results can be easily extended to a large number of systems of physical interest to be discussed in separate publications.

GLOBAL SOLUTIONS TO THE COMPRESSIBLE EULER EQUATIONS WITH GRAVITATIONAL SOURCE

We study the compressible Euler equations in spherical symmetry with a gravitational source surrounding a solid ball. Despite its physical importance, this problem has not received much attention until now. We prove the global existence of weak solutions by constructing approximate solutions and using a modified Godunov scheme. The main point is to obtain a sup-norm bound for the approximate solutions.