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Two-dimensional problem is systematically investigated for the coupled equations in two-dimensional decagonal quasicrystals, and three general solutions are presented by an operator method. To simplify governing equations, each general solution shall take three different forms expressed in terms of three displacement functions, which satisfy partial three differential equations of second order. To illustrate its utility, the closed-form solutions are obtained for problems of point phonon forces and phason force acting at the apex of a quasicrystal wedge, all in terms of the general solutions. Furthermore, these solutions can be degenerated to those of problems of point forces applied on the boundary of a quasicrystal half-plane.

Analyzed in this paper is an investigation of the impacts of the varying source of heat or thermal sink and viscous dissipation on Casson fluid flow from a moving wedge by considering thermal and momentum slips in a mathematical model. Regarding the regulation of concentration fields, we incorporated the Soret and Dufour phenomena. The outcomes are analyzed numerically by using the shooting technique. The governing parametric effects of the flow characteristics are revealed graphically. We also presented the local Sherwood and Nusselt number values for non-Newtonian fluid (Casson fluid) and Newtonian. It is discovered that the thermal and concentration boundary layer is more extensive in Casson fluid while equated with the Newtonian fluid. The thermal and mass transmission in Newtonian fluid is significantly larger than in non-Newtonian fluid. The heat source/sink, Eckert number and Dufour number boost the rate of thermal transport and depreciate the rate of mass transport for both the Newtonian and non-Newtonian fluid cases.

In this analysis, we have considered heat transmission in two-dimensional steady laminar nanofluid flow past a wedge. Magnetohydrodynamic (MHD), Brownian motion, viscous dissipation and thermophoresis effects are considered over the porous surface. Similarity transformations have been used to change the governing partial differential equations (PDEs) into nonlinear higher-order ordinary differential equations (ODEs). Governing ODEs with boundary conditions are then converted to the system of first-order initial value problem. After that the modeled system is solved numerically by RK4 technique. Impact of the magnetic number, Eckert number, Prandtl number, Lewis number, Brownian motion, thermophoresis and permeability parameters on the flow domain is analyzed graphically as well as in tabular form. It is noted that magnitude of Nusselt number for the flow regime increases with the increase of nondimensional parameter $Pr,Nb,Nt$ while opposite behavior is observed in case of R.

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

This study reports both MagnetoHydroDynamics (MHD) and heat generation aspects of a water-based hybrid nanofluid flow with various shapes of the nanoparticles involving Nimonic 80A and ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$, over a moving wedge. Similarity transformations were adapted to obtain non-dimensional equations and solved using MATLAB bvp4c code. All the results and graphs were formulated after a positive outcome of our results with that available in existing literature. Nusselt number, which signifies the heat transfer rate in a flow, increased with an increase in empirical shape factors of the nanoparticle with a contrasting decrease in the drag experienced during the flow, represented by the skin friction coefficient. The velocity profile decreased at a rate of 0.75% for $M=0.6$ to $M=0.8$ due to the augmenting Lorentz forces while it augmented by 18.9% for an augmenting velocity ratio parameter from $R=0.0$ to $R=0.5$ due to the no-slip boundary conditions. Both the Nusselt number and skin friction coefficients decreased with an increase in magnetic parameter. An increase in the nanoparticle concentration resulted in an incrementing streamline value along with increasing temperature profile due to increasing thermal conductivity of the fluid flow system. The physical significance of the study involves in its applications in nuclear, steel industries, MRI scanning for its anti-corrosive and high thermal conductivity properties.

In this paper we study the problems of separability of two disjoint point sets in 3D by multiple criteria extending some notions on separability of two disjoint point sets in the plane.

Lift-gate is a rear closure system present in sports utility vehicles (SUV) and minivans. It has multiple design variables affecting multiple functional requirements. A wedge is a small piece of hardware used to stabilize the lift-gate especially in cross-car direction by providing the load path from the lift-gate to the surrounding structure. But, a wedge may increase the closing effort due to the reaction force in the swing direction. Furthermore, wedges need to accommodate the gap variation to bridge the lift-gate and the body frame. This paper presents the characteristics of two different types of wedges, their effects on the lift-gate system, and design methodologies to improve the wedge performance.

In this study, the effect of the dynamic bike fitting, which was defined as lower limb vertical alignment by inserted wedges, was evaluated. Twelve non-cyclists are participated in this experiment. For comparing pedaling performance between before and after fitting, sub-maximal pedaling tests were conducted for 2 min. The results showed that both the range of motion of the knee joint (medio-lateral direction) which represented pedaling trajectory and the coefficient of variance of pedaling power were decreased in non-cyclists. This result indicated that the dynamic fitting had a positive effect such as increased pedaling kinematic stability and kinetic efficiency on pedaling performance. Supplementary pedaling test was performed by one of the best cyclist, who was a member of the national team and a middle and long distance cyclist. The result of the cyclist test was also similar to the patterns of 12 non-cyclists. It is believed that this study has the meaning of the preliminary study to evaluate the effects of the dynamic fitting. Further study is necessary to evaluate the effects of the fitting through enough subjects and repeated tests by measuring muscle activities and forces.

This paper explores the effect that compression of the conducting particles in Anisotropic Conductive Adhesive (ACA) assemblies has on the resistance of the joints. Particles within the same assembly were compressed by differing amounts by the action of two rigid, planar surfaces which form a wedge with the particles trapped between them. Using this method, it is found that optimum conduction is obtained when metal-coated polymer particles are compressed to a height between 80% and 100% of their original diameters (see Fig. 1 for definitions). Results on flip-chip assemblies with a pitch of 220 μm are presented. They are in agreement with the wedge experiment findings in that larger particles are shown to be able to better accommodate variations in the gap heights between chip and substrate. The wedge experiment has also been used to validate fluid flow based models of particle movement during assembly and statistical models of particle distribution after assembly is complete. The experiments also indicated the presence of thin insulating films between particles which offer an additional safety margin when considering shorting between neighbouring electrodes by clusters of particles.

Some time ago, DeWitt-Morette¹et al. discussed the problem of the propagation of radiation or particles in the presence of a wedge. Their treatment includes path integral solutions of the wedge problem with Dirichlet or Neumann boundary conditions for various situations. Recently, the superconducting phase in a wedge has gained increasing interest. The linearized Ginzburg-Landau equation for the order parameter is formally similar to the Schrödinger equation. But the conditions of no normal current at the boundary pose very specific problems, which are discussed in the present paper.