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Design Equations for Hybrid Systems
Published in Dwight Houweling, Glen T. Daigger, Intensifying Activated Sludge Using Media-Supported Biofilms, 2019
Dwight Houweling, Glen T. Daigger
SymPy is a symbolic math library that is freely distributed for the Python programming language. What is valuable about symbolic math programs is that they allow variables to be treated as symbols, instead of numbers. Design equations can thereby be derived wherein numerical evaluation of parameters can be deferred until the very end. The design equations presented below could not have been developed without it.
Small-Signal Stability Modeling, Sensitivity Analysis, and Parameter Optimization of Improved Virtual Synchronous Machine Based Standalone Inverter
Published in Electric Power Components and Systems, 2023
Deependra Neupane, Nawaraj Poudel
The study begins with the detail mathematical modeling of components of VSM-based inverter. The major components are the power part (inverter circuit) and control part (control dynamics for inverter operation) of inverter circuit, filters, and load. The system of equation defining the dynamics of each component has be adapted from literatures. The system of equation defining the dynamics of control part of VSM are non-linear as they depicts the conventional SM. Hence, the system of equation is linearized using the SYMPY library of python. Keeping the filter, voltage, and load parameters constant, the behavior of system dynamics for different parametric values of SG, VTG, and VE is studied, i.e., parametric sensitivity analysis. The NUMPY and plotting libraries of python has been used for analysis. Finally, the optimization algorithm has been applied to obtain the optimal values of parameters taken under consideration for the maximum system stability. The obtained parameters has been obtained out of the linearized version of the equation, however, the parameters were tested on the actual set system of equations. As a validation of the model and results, the system is built on Simulink using elementary building blocks as shown in Appendix A. The results are compared from both of the scenarios. To summarize, this study is concerned to present the detail mathematical formulation of VSM; both power part and control part, performing the several parameter sensitivity on system stability and optimization of parameters in the context of standalone based inverters.
Double exponential transformation for computing three-center nuclear attraction integrals
Published in Molecular Physics, 2020
In Table 2, we restrict the variable assignments to values that can be handled by a general MATLAB built-in numerical integration function that uses global adaptive quadrature, set to an accuracy of 15 correct digits. However, the MATLAB built-in function is not always able to complete the integral approximation, particularly for large values of and/or . In contrast, the DE transformation method coded in Python (with the help of the symbolic computation package SymPy), was able to complete the approximations. In Table 3 therefore, we restrict the variable assignments to values that cannot be handled by the built-in MATLAB integration function.
Analytical models for stress analysis of real-life bonded joints
Published in The Journal of Adhesion, 2022
Guilherme Garcia Momm, David Fleming
Crocombe[14] incorporated moisture-related degradation of cohesive adhesive properties (Young’s modulus and ultimate stress) into Bigwood’s and Crocombe’s analytical model.[13] Crocombe’s analytical model[14] comprises a boundary value problem (BVP) with a set of six first-order non-linear ODEs. A Python code solved this BVP numerically using finite difference with a collocation algorithm. This code used a symbolic mathematic library (Sympy) and an arbitrary precision library (Mpmath) to implement Bigwood’s and Crocombe’s general elastic analysis[13] as the required initial guess for the numerical solver. Crocombe’s model[14] is referred to as the existing analytical model.