We report the results of a Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear σ model. The notable finding is that it agrees very well with both the prediction inspired by Zamolodchikovs’ S-matrix ansatz and with the continuum limit of the dodecahedron spin model. The latter finding renders the existence of asymptotic freedom in the O(3) model rather unlikely. Asymp...

In this paper we present a new theory of calculus over k-dimensional domains in a smooth n-manifold, unifying the discrete , exterior, and continuum theories. The calculus begins at a single point and is extended to chains of finitely many points by linearity, or superposition. It converges to the smooth continuum with respect to a norm on the space of " monopolar chains, " culminating in the c...

In this paper we present a new theory of calculus over k-dimensional domains in a smooth n-manifold, unifying the discrete , exterior, and continuum theories. The calculus begins at a single point and is extended to chains of finitely many points by linearity, or superposition. It converges to the smooth continuum with respect to a norm on the space of " pointed chains, " culminating in the cha...

Nanotechnology is one of the pillars of human life in the future. This technology is growing fast and many scientists work in this field. The behavior of materials in nano size varies with that in macro dimension. Therefore scientists have presented various theories for examining the behavior of materials in nano-scale. Accordingly, mechanical behavior of nano-plates, nanotubes nano-beams and n...

In this article, the Second Strain Gradient (SSG) theory proposed by Mindlin is used within a Wave Finite Element Method (WFEM) framework for dynamic analysis of one-dimensional Euler–Bernoulli bending beam and torsional bar. Firstly, strong forms continuum models including governing equations boundary conditions torsion cases, respectively, are derived using Hamilton’s principle. New “non-loca...

We examine the excitations of a quasi-one dimensional easy plane antiferromagnet, in a symmetry breaking applied magnetic field. The antiferromagnetic exchange includes a small Dzyaloshinski Moriya component that produces the easy plane. In the classical continuum limit, this system is described by a double-sine-Gordon field theory, which supports soliton excitations and the multi spin wave bou...

the main purpose of this research is to investigate computationally the tautomeric reaction pathway of 5-methyl-3-methylthio-1,2,4-triazole from the thermodynamical and mechanistical viewpoints. in this respect, density functional theory (dft) in conjunction with the quantum theory of atoms in molecule (qtaim) has been employed to model the energetic and electronic features of tautomeric mechan...

Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining the desired classical limit. We examine this “entropy problem” in a model of causal set quantum gravity corresponding to a discretisation of 2D spacetimes. Us...

Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining the desired classical limit. We examine this “entropy problem” in a model of causal set quantum gravity corresponding to a discretisation of 2D spacetimes. Us...