The noncommutative values of quantum observables

We discuss the notion of representing the values of physical quantities by the real numbers, and its limits to describe the nature to be understood in the relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values for a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutative algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex numbers, the idea makes reasonable sense theoretically as well as practically.     

Compact ellipse shaped patch with ground slotted broadband monopole patch antenna for head imaging applications

This paper represents an ellipse-shaped patch with a ground slotted broadband patch antenna for microwave head imaging systems. The proposed antenna constructs with a simple ellipse shaped square patch and modified slotted plane. The proposed design is very simple to fabricate and is enclosed in a microwave imaging system. The slotted patch, and the partial ground plane improves the antenna's efficiency, operating frequency range, and gain. The size of the proposed antenna is 70 × 60 × 1.5 mm³ with the electrical dimension being 0.277λ × 0.238λ × 0.006λ at a lower frequency of 1.19 GHz and connected to a 50Ω microstrip feeding line. This antenna is printed onto a low-cost FR-4 substrate whose relative permittivity is 4.4, and whose thickness is 1.5 mm. CST and HFSS software have been used for simulation and thereafter successful completion of the measurements and the fabrication. The comprehensive simulation exhibits that this design provides a bandwidth of 2.37 GHz (1.19 – 3.56 GHz) and 100% of the fractional bandwidths (% BW) with the reflection coefficient of <-10 dB. This antenna on FR-4 can produce an average gain of around 3.63 dBi with 5.95 dBi peak gain at whole operation frequencies. The prototype has a peak radiation efficiency of approximately 97% across the active frequency spectrum with 93% of average. The antenna does have an improved fidelity-factor (> 90 %) with a shorter group-delay. Several design modifications have been performed to get perfect, effective, and suitable results for microwave imaging applications. A 3D-realist Hugo head model is fitted with a single antenna and a 9-antenna array component to verify the performance of both the single antenna, and the configured array antenna. The antenna penetrates the brain human tissues satisfactorily. Across the operational range, the specific absorption rate (SAR) attains a limit of <1 W/kg. The analysis of both numeric and experimental evidence clearly indicates that the suggested antenna is ideal for microwave head-imaging implementations.     

Weak dissipation of electrostatic solitary structures in warm collisional pair-ion plasmas with non-Maxwellian electron population

The localized electrostatic structures with dissipation due to ion-neutral collisions in a symmetric warm pair-ion plasma in the presence of non-Maxwellian population of electrons are studied. The analytical model for ion dynamics is based on fluid equations and the evolution equation is derived by using the reductive perturbation scheme in the form of a damped Korteweg-de Vries equation. The parameter regime relevant to space-based observations and laboratory plasmas is considered and time evolution of the propagating ion-acoustic soliton is discussed. The energetic-particles-driven properties of soliton for various spectral indices, dissipation, ion temperature, and density are illustrated with comparison to the thermal mode for Boltzmann distribution of electrons.     

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.     

Magnetohydrodynamics (MHD) axisymmetric flow and heat transfer of a hybrid nanofluid past a radially permeable stretching/shrinking sheet with Joule heating

The main interest of the present work is to fundamentally investigate the flow characteristics and heat transfer of a hybrid Cu-Al₂O₃/water nanofluid due to a radially stretching/shrinking surface with the mutual effects of MHD, suction and Joule heating. The surface is permeable to physically allow the wall mass fluid suction. Tiwari and Das model of nanofluid is used with the new thermophysical properties of hybrid nanofluid to represent the problem. A similarity transformation is adopted to convert the governing model (PDEs) into a nonlinear set of ordinary differential equations (ODEs). A bvp4c solver in MATLAB software is employed to numerically compute the transformed system. The numerical results are discussed and graphically manifested in velocity and temperature profiles, as well as the skin friction coefficient and heat transfer rate with the pertinent values of the dimensionless parameters namely magnetic, Cu volume fraction, suction and Eckert number. The Eckert number has no impact on the boundary layer separation while the higher value of the suction parameter may affect the heat transfer performance. The presence of dual solutions (first and second) is seen on all the profiles within a limited range of the physical parameters. The stability analysis is executed, and it is validated that the first solution is the real solution.     

Nickel sulphide-reduced graphene oxide composites as counter electrode for dye-sensitized solar cells: Influence of nickel chloride concentration

Nickel sulphide-reduced graphene oxide (NiS-rGO) composite films have been prepared via modified Hummers’s method assisted with spin coating technique. The NiS-rGO samples were then employed as counter electrode in a dye-sensitized solar cell (DSSC). The main aim of this work is to investigate the relationship between the concentrations of NiCl₂ with the properties of NiS-rGO and performance parameters of the device. The dominant rGO and minor NiS phase exist in the composite. The morphology of the composite is white strips rGO and NiS agglomerate particle. The element of C, O, Ni and S present in the composite. The highest η of 1.04% and J_sc of 7.39 mA cm⁻² were obtained from the device with 0.06 M NiCl₂ resulted from the longest carrier lifetime. The photovoltaic parameters results reveal that NiS-rGO composite has potential to become as a free platinum counter electrode of DSSC.     

Influence of metallic nanoparticles in water driven along a wavy circular cylinder

In the present study, simultaneous effects of metallic nanoparticles and magnetohydrodynamic due to stagnation point flow of nanofluid along a wave circular cylinder is presented. The effect of induced magnetic field is incorporated to deal the boundary and thermal boundary layer domain. Mathematical modelling for momentum and energy equation is constructed that is based upon three different kinds of nanoparticles namely: copper (Cu), Titanium di oxide (TiO₂), and alumina (Al₂O₃) within the working fluid water. Each mixture is analysed at the individual level and made comparison amongst all the mixture to examine the resistance and thermal conductivity of nanofluid within the boundary layer region. The solutions are exposed via boundary value problem using shooting method along with the Runge-Kutta-Fehlberg method. The characteristics of emerging parameters for the fluid flow and heat transfer are discussed through graphs and tables. The effects of ϕ (nanoparticle volume fraction) on heat transfer and shear stress at the wall are analysed in detail. It is finally concluded that by increasing the ratio of nanoparticles there is a significant increase in the temperature but slight decrease in the velocity profile.