A discrete Frenkel-Kontorova model with two alternate spring constants k1 and k2 is studied. It is found that this model has many surprising behaviours. The continuum version of this model is different from the sine-Gordon equation, the continuum version of the standard FK model. More interestingly, it has an unpinned commensurate phase which is translationally invariant. A phase transition tak...

Phase fitting has been extensively used during the last years to improve the behaviour of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian integrators. The results show improved accuracy and total energy behaviour in Hamiltonian systems. Numerical tests on the long term integration (10 periods) of the 2-...

explosion has always been regarded as one of the most complicated engineering problems. as a result, many engineers have preferred rather simplified empirical approaches in comparison to extremely complex deterministic analyses. in this paper, however, a numerical simulation based on the combined finite/discrete element methodology is presented for analyzing the dynamic behavior of fracturing r...

the modified nrtl (m-nrtl) model is used to represent the excess gibbs free energy of aqueous (alcohol + electrolyte) solutions. in this work, the m-nrtl model previously developed for representation of vapor-liquid equilibria for (polymer + salt + water) systems has been extended to represent liquid-liquid equilibria of (alcohol + salt + water) systems. the proposed extension is a modified of ...

in this article, the discrete time state space model with first-order autoregressive dependent process noise is considered and the recursive method for filtering, prediction and smoothing of the hidden state from the noisy observation is designed. the explicit solution is obtained for the hidden state estimation problem. finally, in a simulation study, the performance of the designed method ...

We consider systems with continuous spins and annealed dilution. We show that, as in the discrete case, such systems often undergo a phase transition, which is manifested in the appearance of a staggered intermediate phase. In particular, these phases appear in systems such as the massive Gaussian model where there is no phase transition in the undiluted system.

An argument is presented to explain the fact that the same mean-field results apply to several spin glass models, such as the 'random-energy' model and the large-p Potts glass model. The dilute simplest spin glass model is solved, yielding the same mean-field results. The argument is based on the fact that the symmetry of the discrete-spin system can be determined by the discrete-spin type or b...

I present ongoing developments on hybrid models which combine the potential model, for the description of the background, with the R-matrix model, for the description of discrete states. Physical parameters of discrete states are converted into formal R-matrix parameters, taking into account the potential background. The nuclear part of this potential is constructed by a new variant of an inver...

We study the full unitary matrix models. Introducing a new term l logU , l plays the role of the discrete time. On the other hand, the full unitary matrix model contains a topological term. In the continuous limit it gives rise to a phase transition at θ = π. The ground state is characterize by the discrete time l. The discrete time l plays like the instanton number.