Rotating 3D Flow of Hybrid Nanofluid on Exponentially Shrinking Sheet: Symmetrical Solution and Duality

This article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina (Al2O3), and copper (Cu) as solid nanoparticles. The system of governing partial differential equations (PDEs) was transformed by an exponential similarity variable into the equivalent system of ordinary differential equations (ODEs). By applying a three-stage Labatto III-A method that is available in bvp4c solver in the Matlab software, the resultant system of ODEs was solved numerically. In the case of the hybrid nanofluid, the heat transfer rate improves relative to the viscous fluid and regular nanofluid. Two branches were obtained in certain ranges of the involved parameters. The results of the stability analysis revealed that the upper branch is stable. Moreover, the results also indicated that the equations of the hybrid nanofluid have a symmetrical solution for different values of the rotation parameter (Ω).

Symmetrical or Non-Symmetrical Debonds at Fiber–Matrix Interfaces: A Study by BEM and Finite Fracture Mechanics on Elastic Interfaces

A recently proposed criterion is used to study the behavior of debonds produced at a fiber–matrix interface. The criterion is based on the Linear Elastic–(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Special attention is given to the discussion about the symmetry of the debond onset and growth in an isolated single fiber specimen under uniaxial transverse tension. A common composite material system, glass fiber–epoxy matrix, is considered. The present methodology uses a two-dimensional (2D) Boundary Element Method (BEM) code to carry out the analysis of interface failure. The present results show that a non-symmetrical interface crack configuration (debonds at one side only) is produced by a lower critical remote load than the symmetrical case (debonds at both sides). Thus, the non-symmetrical solution is the preferred one, which agrees with the experimental evidences found in the literature.

UNIQUENESS OF POSITIVE RADIAL-SYMMETRICAL SOLUTION OF DIRICHLET PROBLEM IN ANNULAR DOMAINS FOR ONE CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER

The existence and uniqueness of positive radially symmetric solution of Dirichlet problem in annular domain for one class of nonlinear differential equations of the second order is proved.

PASSAGE OF RADIATION THROUGH WORMHOLES

We investigate numerically the process of the passage of a radiation pulse through a wormhole and the subsequent evolution of the wormhole that is caused by the gravitational action of this pulse. The initial static wormhole is modeled by a spherically symmetrical solution with zero mass. The radiation pulses are modeled by spherically symmetrical shells of self-gravitating massless scalar fields. We demonstrate that the compact signal propagates through the wormhole and investigate the dynamics of the fields in this process for both cases: collapse of the wormhole into the black hole and for the expanding wormhole.

Thermal Convection Bifurcation Within Isosceles Triangular Cavities

Laminar thermal convection of air confined to an isosceles triangular cavity heated from the base and symmetrically cooled from the upper inclined walls has been investigated numerically. The system of transient conservation equations, subject to the proper boundary conditions, along with the equation of state assuming the air behaves as a perfect gas are solved with the finite volume method. In the conservation equations, the second-order-accurate QUICK scheme was used for the discretization of the convective terms and the SIMPLE scheme for the pressure-velocity coupling. The maximum height-to-base aspect ratio A is fixed at 0.5, while the Grashof number extends from a low Gr = 103 to a high Gr = 106. The influence of Gr on the flow and temperature patterns is analyzed and discussed for two opposing scenarios, one corresponds to increasing Gr and the other corresponds to decreasing Gr. It is found that two steady-state solutions are possible, excluding their solution images through a vertical mirror plane. The symmetrical solution prevails for relatively low Grashof numbers. However, as the Gr is gradually increased, a transition occurs at a critical value of Gr. Above this critical value of Gr, an asymmetrical solution exhibiting a pitchfork bifurcation arises and eventually becomes steady. The existing ranges of these unsteady and steady solutions are reported for the two opposing scenarios. Also, issues related to the observed hysteresis phenomenon are discussed in detail.

Kcsa

Ion conduction and selectivity properties of KcsA, a bacterial ion channel of known structure, were studied in a planar lipid bilayer system at the single-channel level. Selectivity sequences for permeant ions were determined by symmetrical solution conductance (K+ > Rb+, NH4+, Tl+ ≫ Cs+, Na+, Li+) and by reversal potentials under bi-ionic or mixed-ion conditions (Tl+ > K+ > Rb+ > NH4+ ≫ Na+, Li+). Determination of reversal potentials with submillivolt accuracy shows that K+ is over 150-fold more permeant than Na+. Variation of conductance with concentration under symmetrical salt conditions is complex, with at least two ion-binding processes revealing themselves: a high affinity process below 20 mM and a low affinity process over the range 100–1,000 mM. These properties are analogous to those seen in many eukaryotic K+ channels, and they establish KcsA as a faithful structural model for ion permeation in eukaryotic K+ channels.

Single Na+ channels activated by veratridine and batrachotoxin.

Voltage-sensitive Na+ channels from rat skeletal muscle plasma membrane vesicles were inserted into planar lipid bilayers in the presence of either of the alkaloid toxins veratridine (VT) or batrachotoxin (BTX). Both of these toxins are known to cause persistent activation of Na+ channels. With BTX as the channel activator, single channels remain open nearly all the time. Channels activated with VT open and close on a time scale of 1-10 s. Increasing the VT concentration enhances the probability of channel opening, primarily by increasing the rate constant of opening. The kinetics and voltage dependence of channel block by 21-sulfo-11-alpha-hydroxysaxitoxin are identical for VT and BTX, as is the ionic selectivity sequence determined by bi-ionic reversal potential (Na+ approximately Li+ greater than K+ greater than Rb+ greater than Cs+). However, there are striking quantitative differences in open channel conduction for channels in the presence of the two activators. Under symmetrical solution conditions, the single channel conductance for Na+ is about twice as high with BTX as with VT. Furthermore, the symmetrical solution single channel conductances show a different selectivity for BTX (Na+ greater than Li+ greater than K+) than for VT (Na+ greater than K+ greater than Li+). Open channel current-voltage curves in symmetrical Na+ and Li+ are roughly linear, while those in symmetrical K+ are inwardly rectifying. Na+ currents are blocked asymmetrically by K+ with both BTX and VT, but the voltage dependence of K+ block is stronger with BTX than with VT. The results show that the alkaloid neurotoxins not only alter the gating process of the Na+ channel, but also affect the structure of the open channel. We further conclude that the rate-determining step for conduction by Na+ does not occur at the channel's "selectivity filter," where poorly permeating ions like K+ are excluded.