We propose a minimum principle to derive a QM/MM (quantum-mechanical/molecular-mechanical) method from the first principle. We approximate the Hamiltonian of a spectator substituent as the structure-dependent effective Hamiltonian in a least-squares sense. This effective Hamiltonian is expanded with the orthogonal operator set called the normal-ordered product. We determine the structure-depend...

The finite element method is a numerical method for obtaining approximate solutions for boundary value problems that are defined in terms of a set of governing mathematical equations, boundary (and/or initial conditions), constitutive laws and other secondary relations such as the strain-displacement relations. In general, a number of different principles (e.g., virtual work principle, minimum ...

The finite element method is a numerical method for obtaining approximate solutions for boundary value problems that are defined in terms of a set of governing mathematical equations, boundary and/or initial conditions, constitutive laws and other secondary relations such as the strain-displacement relations. In general, any one of a number of different principles (e.g., virtual work principle,...

Variable Stiffness Actuators (VSA) are currently being regarded as promising actuator types in robotics research especially due to their capability to store potential energy in their elastic elements and to control this energy by altering the elastic properties of these elements. The controllable potential energy enables these actuators to outperform their rigid counterparts especially when rea...

We have used a variational approach to calculate some thermodynamic properties of the quasi-one dimensional liquid 3He such as the energy, entropy, free energy, equation of state and heat capacity at finite temperature. We have employed the Lennard-Jones potential as the inter-atomic interaction. We have seen that the total energy increases by increasing both temperature and density....

As a droplet moves, due to evaporation at the surface, the droplet size is gradually reduced. Due to decreasing the size of the droplets moving in the spray core, the surface charges become closer and the repulsive force between the charges increases. When the Coulombic force overcomes the surface tension force (Rayleigh instability) the droplet breaks into smaller droplets (Coulomb fission). T...

From the point of view modeling internal structure Earth, its figure and evolution play an important role, which to one degree or another are associated with gravitational energy principle minimization. The realization minimum potential for models distribution Earth’s density is key in studies on detection inhomogeneous mass distribution. Achieving Earth equivalent approximation hydrostatic sta...