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Abstract. Two different types of orthogonality condition models (OCM) are equivalently formulated in the Faddeev formalism. One is the OCM which uses pairwise orthogonality conditions for the relative motion of clusters, and the other is the one which uses the orthogonalizing pseudo-potential method. By constructing a redundancy-free T -matrix, one can exactly eliminate the redundant components of the total wave function for the harmonic-oscillator Pauli-forbidden states, without introducing any limiting procedure. As an example, a three-α-particle model interacting via the deep αα potential by Buck, Friedrich and Wheatley is investigated.

SUMMARYThe governing equation of elasticity is discretized into motion equations of the particles in a Hamiltonian system. A weighted least-square method is adopted to evaluate the Green-Lagrange strain. Using a symplectic scheme for the Hamiltonian system, we obtain the property of energy conservation in the discretized calculations. However, local particle oscillations occur, and they excessively decrease low frequency motion. In this study, we propose the use of an artificial potential force to suppress the local oscillations. The accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation. With the inclusion of the artificial force, the local oscillations are reduced while energy conservation is maintained.

SUMMARYParticle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles. They have a great degree of flexibility, for instance, in dealing with complex large deformations or the fragmentation of solids. In this paper, a particle method for non-linear elastodynamics of compressible and incompressible materials is developed based on a discretization of the Lagrangian from which the governing equations of elastodynamics are derived using the principle of least action. The discretized Lagrangian leads to a finite-dimensional Hamiltonian system via the Legendre transformation. If the material is incompressible, the Hamiltonian system is accompanied by holonomic constraints. Depending on whether the material is compressible or incompressible, the symplectic scheme adopted for numerical time integration is either the Störmer/Verlet scheme or the RATTLE method, respectively. The resulting particle method inherits the symplectic structure possessed by the governing equations of elastodynamics. In the case of incompressible materials, incompressibility is strictly enforced at each time step. Some numerical tests indicate the excellence of the method for conservation of mechanical energy besides that of linear and angular momenta.