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 expecte...

fiber/ metal laminates (fmls) are hybrid composites consisting of alternating thin layers of metal sheets and fiber reinforced epoxy laminates. in this study, the effect of fiber orientation on impact properties of fml plates is investigated both analytically and experimentally. two groups of specimens were prepared and tested in two different levels of impactor energy. the indentation depth an...

The purpose of this paper is to provide an a]ternate statement of the Pontryagin maximum principle as applied to systems which are most conveniently and naturally described by matrix, rather than vector, differential or difference equations. The use of gradient matrices facilitates the manipulation of the resultant equations. The ~heory is applied to the solution of a simple optimization problem.

A conforming finite element discretization of the pure traction elasticity boundary value problem results in a singular linear system of equations. The singularity of the linear system is removed through various approaches. In this report, we consider an alternative approach in which discrete finite element formulations are derived directly from the principle of minimum potential energy. This p...

in this paper, finding dynamic load carrying capacity (dlcc) of flexible link manipulators in point to-point motion was formulated as an optimal control problem. the finite element method was employed for modelling and deriving the dynamic equations of the system. the study employed indirect solution of optimal control for system motion planning. due to offline nature of the method, many diffic...

1-dimensional hamiltonian with ionization energy (ξ) is shown to be exactly the same with the total energy from the standard harmonic oscillator hamiltonian, with the harmonic oscillator potential, mωx/2. Commutation relations for the ladder operators, energy at the n state and the expectation value for the potential are analyzed and shown to be consistent with the principle of ξ. We also deriv...

A numerical method is presented for stability analysis of cable–bar structures. An optimization problem is formulated to find the minimum value of the incremental total potential energy that depends on the direction of the incremental displacements. The penalty method with slack variables is used for representing the discontinuity in member stiffness. The tangent stiffness matrix is shifted to ...

We characterize the property of obtaining a solution to a convex program by minimizing over the feasible region a linearization of the objective function at any of its solution points (Minimum Principle Sufficiency). For the case of a monotone linear complementarity problem this MPS property is completely equivalent to the existence of a nondegenerate solution to the problem. For the case of a ...

In this communication we propose and also verify through ab initio calculations a new electronic structure principle, viz. the minimum magnetizability principle (MMP), to extend the domain of applicability of the conceptual density functional theory (DFT) 1 in explaining the magnetic interactions and magnetochemistry. This principle may be stated as, “A stable configuration/conformation of a mo...

Estimation of the height of caved and fractured zones above a longwall panel along with the stability conditions of the goaf area are very crucial to determine the abutment stresses, ground subsidence, and face support as well as designing the surrounding gates and intervening pillars. In this work, the height of caving-fracturing zone above the mined panel is considered as the height of destre...