Dual Penta-Compound Combination Anti-Synchronization with Analysis and Application to a Novel Fractional Chaotic System

This paper studies a fractional-order chaotic system with sine non-linearities and highlights its dynamics using the Lyapunov spectrum, bifurcation analysis, stagnation points, the solution of the system, the impact of the fractional order on the system, etc. The system considering uncertainties and disturbances was synchronized using dual penta-compound combination anti-synchronization among four master systems and twenty slave systems by non-linear control and the adaptive sliding mode technique. The estimates of the disturbances and uncertainties were also obtained using the sliding mode technique. The application of the achieved synchronization in secure communication is illustrated with the help of an example.

Complex singularity analysis for vortex layer flows

We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are characterized by intense vorticity concentrated around a curve. In addition to their intrinsic interest, vortex layers are relevant configurations because they are regularizations of vortex sheets. In this paper, we consider vortex layers whose thickness is proportional to the square-root of the viscosity. We investigate the typical roll-up process, showing that crucial phases in the initial flow evolution are the formation of stagnation points and recirculation regions. Stretching and folding characterizes the following stage of the dynamics, and we relate these events to the growth of the palinstrophy. The formation of an inner vorticity core, with vorticity intensity growing to infinity for larger Reynolds number, is the final phase of the dynamics. We display the inner core's self-similar structure, with the scale factor depending on the Reynolds number. We reveal the presence of complex singularities in the solutions of Navier–Stokes equations; these singularities approach the real axis with increasing Reynolds number. The comparison between these singularities and the Birkhoff–Rott singularity seems to suggest that vortex layers, in the limit $Re\rightarrow \infty$ , behave differently from vortex sheets.

Aqueous aluminium–copper hybrid nanofluid flow past a sinusoidal cylinder considering three-dimensional magnetic field and slip boundary condition

We analyzed the problem of the steady general three-dimensional magnetohydrodynamics stagnation-point boundary layer flow past an impermeable wavy circular cylinder considering aluminium–copper/water hybrid nanofluid as the working fluid and velocity slip as well as temperature jump boundary conditions. The induced magnetic field effect was also taken into account. The analytical procedure is based on the model that implements the nanoparticles and base fluid masses to formulate the equivalent volume fraction, equivalent density, and equivalent specific heat at constant pressure which is then substituted in the chosen single-phase thermophysical properties. Then, the foregoing relations were used in basic governing PDEs (partial differential equations), according to Tiwari–Das nanofluid scheme. It is worth mentioning that the bvp4c code from MATLAB software that is a famous finite-difference method has been exploited for solving the final similarity ODEs (ordinary differential equations). Results demonstrate that the developed mass-based model can be successfully employed with great confidence to study the flow and heat transfer of hybrid nanofluid in other similar problems. Moreover, it is proved that the nodal stagnation points possess higher values of skin friction coefficients and local Nusselt numbers relative to those for the saddle stagnation points. Besides, enhancing the second nanoparticle's mass leads to increase in all parameters of engineering interest including skin friction coefficients along x and y directions as well as local Nusselt number.

Stagnation points control chaotic fluctuations in viscoelastic porous media flow

Viscoelastic flows through porous media become unstable and chaotic beyond critical flow conditions, impacting widespread industrial and biological processes such as enhanced oil recovery and drug delivery. Understanding the influence of the pore structure or geometry on the onset of flow instability can lead to fundamental insights into these processes and, potentially, to their optimization. Recently, for viscoelastic flows through porous media modeled by arrays of microscopic posts, Walkama et al. [D. M. Walkama, N. Waisbord, J. S. Guasto, Phys. Rev. Lett. 124, 164501 (2020)] demonstrated that geometric disorder greatly suppressed the strength of the chaotic fluctuations that arose as the flow rate was increased. However, in that work, disorder was only applied to one originally ordered configuration of posts. Here, we demonstrate experimentally that, given a slightly modified ordered array of posts, introducing disorder can also promote chaotic fluctuations. We provide a unifying explanation for these contrasting results by considering the effect of disorder on the occurrence of stagnation points exposed to the flow field, which depends on the nature of the originally ordered post array. This work provides a general understanding of how pore geometry affects the stability of viscoelastic porous media flows.

Flow characteristics analysis for flow past the porous spheres: wake structures and drag force coefficients

Flow past a permeable sphere is different from that of a solid sphere due to the penetration of the fluid within porous structures, which can arise a change of flow fields. In this work, flow past porous spheres with Darcy numbers (Da) ranging from [0,10−3 ] were measured using planar Particle Image Velocimetry (PIV). The whole flow fields, including both leading edge and trailing edge, were captured at six different Reynolds numbers (Re) varying from 400 to 1400. Time-average flow fields were calculated based on instantaneous flow fields within fully-developed stages. Local minimum method was used to search for stagnation point positions. The results show positions of stagnation points are nearly proportional to the logarithm of Re. For most porous spheres, positions of stagnation points are extended to farther downstream positions than that of a solid sphere. However, at some certain Darcy numbers, ranging from 5 ∗ 10−6 to 2 ∗ 10−5, positions of stagnation points are closer to the sphere centers than that of an impermeable one.

An alternative approach to study irrotational periodic gravity water waves

We are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

Water Stagnation and Flow Obstruction Reduces the Quality of Potable Water and Increases the Risk of Legionelloses

Legionella is an opportunistic waterborne pathogen associated with Legionnaires' disease and Pontiac fever. Despite improved public awareness, the incidence of Legionella associated infections has been increasing. Aerosols generated from engineered potable water systems are a demonstrated cause of both nosocomial and community-acquired legionellosis. The ecology of Legionella in these systems is complex with multiple factors impacting their colonization and persistence. Flow dynamics has been identified as an important factor and stagnation in cooling towers is an accepted risk for increased Legionella growth; however, less is known about the impact of flow dynamic on Legionella in potable water systems. This is especially complex due to the inherent intermittent and variable usage observed within outlets of a potable water system. This systematic literature review examines the role of fluid dynamics and stagnation on the colonization and growth of Legionella in potable water systems. Twenty two of 24 identified studies show a positive association between stagnation zones and increased colonization of Legionella. These zones included dead legs, dead ends, storage tanks, and obstructed water flow (such as intermittent usage or flow restriction). Prolonged stagnation in building plumbing systems also deteriorates the quality of thermally or chemically treated potable water. This stimulates the colonization of Legionella established biofilms. Such biofilms are intrinsically resistant to disinfection procedures and accelerate the rate of decay of chemical disinfectants. Sub-lethal doses of disinfectants and the presence of protozoan hosts in stationary water promote generation of viable but non-culturable Legionella cells. This results in false negatives in surveillance methods that use culture methodology. In conclusion, elimination of temporal and permanent stagnation points can improve the quality of potable water, efficacy of disinfectants, and reduce the risk of legionellosis. Current guidelines and water safety plans recognize the risks associated with permanent stagnation point (dead ends and dead legs); however, there is a need for greater emphasis on controlling temporal stagnation arising from intermittent usage.