Zigzag carbon nanotubes—Molecular/structural mechanics and the finite element method

Quantum Mechanics and the Finite Element Method

dx = 0 (1) Here ψ(x) is some sort of wavefunction that somehow describes the properties of the particle, V (x) is the potential the particle moves in, and E is the particle energy. The term ∇ψ(x) ·∇ψ(x) measures the curvature of the wavefunction. In some way it is a surrogate for the (kinetic) energy of the particle. Schrödinger never came to terms with the physical meaning of ψ(x). From this e...

From Wave Mechanics to Matrix Mechanics: The Finite Element Method

There are only a few analytic solutions available for this partial differential equation. Schrödinger found all of the most useful ones in his first paper on Quantum Mechanics: the Coulomb potential and the harmonic oscillator potential. He published the solution to the nonrelativistic Coulomb problem in his first Wave Mechanics paper but solved the relativistic problem six months earlier. He a...

Carbon Nanotubes Under Simple Tension and Torsion – Molecular/Structural Mechanics and the Finite Element Method

Finite element method for finite-size scaling in quantum mechanics.

We combined the finite-size scaling method with the finite element method to provide a systematic procedure for obtaining quantum critical parameters for a quantum system. We present results for the Yukawa potential solved with the finite element approach. The finite-size scaling approach was then used to find the critical parameters of the system. The critical values lambda c, alpha, and nu we...

Fracture Mechanics Analysis of Fourth Lumbar Vertebra in Method of Finite Element Analysis

Objective: In this paper, finite element model of the L4 vertebra subjected to combination of compression and flexion loading in isotropic and anisotropic cases is investigated. Methods: In both cases, the vertebra is considered homogeneous. Also, the body of vertebra is divided to cancellous and cortical sections in anisotropic model, but the process is assumed isotropic such as isotropic mode...