Using spreadsheets in chemical education to avoid symbolic mathematics.

Traditionally, quantum theory has traditionally relied heavily on the use of  mathematics. However, there is a significant cohort of students who are  weak in mathematics, for example, students who are majoring in   biochemistry, biological sciences, etc. This paper reports on the use of  spreadsheets to generate approximate numerical solutions and visual  (graphical) descriptions as a method of avoiding or minimizing symbolic  manipulations, mathematical derivations and numerical computation. A  specific example from quantum theory is provided. Some aspects of  educational pedagogy of spreadsheet usage are discussed.

A comprehensive analytical subdomain model and its field solutions for surface-mounted permanent magnet machines

This paper presents a comprehensive analytical subdomain model together with its field solutions for predicting the magnetic field distributions in surface-mounted permanent magnet (PM) machines. The tooth tips and slotting effects during open-circuit, armature reaction, and on-load conditions are considered when deriving the model and developing its solutions. The model derivations and field solutions are extended from a previous model, and can be applied to PM machines with any combinations of slot and pole numbers and any magnetization patterns in the magnets. This model is initially formulated according to Laplace's and Poisson's equations in 2-D polar coordinates by the separation of variables technique in four subdomains, such as magnet, airgap, winding slots, and slot-openings. The field solution of each subdomain is obtained applying the appropriate boundary conditions and interface conditions between every two subdomains, respectively, which can precisely account for the mutual influence between slots. Finite element analysis (FEA) is later deployed to validate the analytical results in a surface-mounted PM machine that has nonoverlapping winding arrangement. For validation purposes, PM machines having 3-slot/2-pole with parallel magnetization and 12-slot/10-pole with either parallel or radial magnetizations are used for comparisons. Computation of global quantities for the motor which include the phase back-EMF and cogging torque is also included. The results indicate that the proposed analytical model can accurately predict the magnetic field distributions in each subdomain and the motor's global quantities, which are in good agreement with those obtained from the FEA.

A game-theoretic resource allocation approach for intercell device-to-device communications in cellular networks

Device-to-Device (D2D) communication is a recently emerged disruptive technology for enhancing the performance of current cellular systems. To successfully implement D2D communications underlaying cellular networks, resource allocation to D2D links is a critical issue, which is far from trivial due to the mutual interference between D2D users and cellular users. Most of the existing resource allocation research for D2D communications has primarily focused on the intracell scenario while leaving the intercell settings not considered. In this paper, we investigate the resource allocation issue for intercell scenarios where a D2D link is located in the overlapping area of two neighboring cells. Specifically, We present three intercell D2D scenarios regarding the resource allocation problem. To address the problem, we develop a repeated game model under these scenarios. Distinct from existing works, we characterize the communication infrastructure, namely Base Stations (BSs), as players competing resource allocation quota from D2D demand, and we define the utility of each player as the payoff from both cellular and D2D communications using radio resources. We also propose a resource allocation algorithm and protocol based on the Nash equilibrium derivations. Numerical results indicate that the developed model not only significantly enhances the system performance including sum rate and sum rate gain, but also sheds lights on resource configurations for intercell D2D scenarios.