in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited sc...

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/ √ t, for the energy current correlation in equil...

We investigate a lattice scalar field theory in the presence of a bias favouring the establishment of an energy current, as a model for stationary nonequilibrium processes at low temperature in a non-integrable system. There is a transition at a finite value of the bias to a gapless modulated phase which carries a classical current; however, unlike in similar, integrable, models, quantum effect...

The distinct nature of the cold fusion regime is emphasized: electromagnetic selection rules suppress radiation, permitting excess energy transference to the lattice; the coherent nature of the wave-function is at variance with the standard separation between barrier penetration and nuclear reactivity. The discussion is restricted to tritium production, based on the dd reaction that populates t...

Mixed convection of Cu-Water nanofluid is studied numerically in a shallow inclined enclosure by applying lattice Boltzmann method. The D2Q9 lattice and internal energy distribution function based on the BGK collision operator are used in order to develop the thermal flow field. The enclosure's hot lid has the constant velocity of U0 while its cold lower wall has no motion. Moreover, sidewalls ...

The PEP-N project at SLAC [1] consists of a Very Low-Energy small electron Ring (VLER) that will collide with the low-energy 3.1 GeV positron beam (LER) of PEP-II, producing center-of-mass energies between the 1.1 GeV and the J/ψ . The beams will collide head-on and will be separated in the detector magnetic field which is part of the Interaction Region [2]. The IP β functions were chosen such ...

Zero-point energy (ZPE) can be thought of as a limitless source of potential energy that exists throughout the universe; in essence, ZPE describes the ground state of a quantum mechanical system that exhibits a fluctuating finite energy due to Heisenberg’s uncertainty principle. Quantum mechanics predicts that all of space must be filled with electromagnetic zero-point fluctuations (also called...

We investigate certain connections between the continuum and atomistic descriptions of deformable crystals, using some interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with general binary interactions in two dimensions. A new bond counting approach is used, which reduces the problem to the lattice point problem of number th...