What does low energy physics tell us about the zero momentum gluon propagator

The connection between QCD, a nonlocal Nambu–Jona-Lasinio type model and the Landau gauge gluon propagator is explored. This two point function is parameterized by a functional form which is compatible with Dyson–Schwinger and lattice QCD results. Demanding the nonlocal model to reproduce the experimental values for the pion mass, the pion decay constant, Γ_π→γγ${\Gamma }_{\pi \to \gamma \gamma }$ and the light quark condensate we conclude that low energy physics does not distinguish between the so-called decoupling and scaling solutions of the Dyson–Schwinger equations. This result means that, provided that the model parameters are chosen appropriately, one is free to choose any of the above scenarios. Furthermore, the nonlocal Nambu–Jona-Lasinio quark model considered here is chiral invariant and satisfies the GMOR relation at the 1% level of precision.     

Phenomenological interatomic potentials for silicon, germanium and their binary alloy

A phenomenological potential is constructed for silicon, germanium, and their binary alloy. As in the modified embedded atom model (MEAM), the interatomic interactions are assumed to arise from the overlap of the electron wave functions. However, the calculation of energy is quite different in the two models. The proposed potential has seven adjustable parameters in contrast to ten or more in MEAM but gives perfect fit with the measured values of seven most important quantities for characterizing strained silicon: cohesive energy, equilibrium lattice constant, vacancy formation energy, Raman frequency, and the three elastic constants. The potential should be suitable for lattice statics calculations on strained silicon.     

A new lattice model of traffic flow with the consideration of the driver?s forecast effects

In this Letter, a new lattice model is presented with the consideration of the driver?s forecast effects (DFE). The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the new model can improve the stability of traffic flow by considering DFE. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis. Numerical simulation also shows that the new model can improve the stability of traffic flow by adjusting the driver?s forecast intensity parameter, which is consistent with the theoretical analysis.     

Hydrogen storage: Lattice dynamics of orthorhombic NaMgH3

In this work, we investigate the structural, dynamic and thermodynamic properties of NaMgH₃, devoted for hydrogen storage. Density functional theory using pseudopotential methods and generalized gradient approximation has been used. A good agreement between the calculated structural parameters and the experimental data was found. A linear-response approach for the density functional theory is used in order to derive the Born effective charge tensors, the dielectric permittivity tensors, the phonon frequencies at the center of the Brillouin zone, the phonon-dispersion curves and the corresponding density of states for NaMgH₃ material. The obtained phonon frequencies at the zone center (Γ point) for the Raman-active and infrared-active modes are analyzed. Thermodynamic functions using the phonon density of states are also calculated.     

Large Sets of Lattices without Order Embeddings

Let I and μ be an infinite index set and a cardinal, respectively, such that |I| ≤ μ and, starting from ?₀, μ can be constructed in countably many steps by passing from a cardinal λ to 2^λ at successor ordinals and forming suprema at limit ordinals. We prove that there exists a system X = {L_i: i ∈ I} of complemented lattices of cardinalities less than |I| such that if i, j ∈ I and φ: L_i → L_j is an order embedding, then i = j and φ is the identity map of L_i. If |I| is countable, then, in addition, X consists of finite lattices of length 10. Stating the main result in other words, we prove that the category of (complemented) lattices with order embeddings has a discrete full subcategory with |I| many objects. Still in other words, the class of these lattices has large antichains (that is, antichains of size |I|) with respect to the quasiorder “embeddability.” As corollaries, we trivially obtain analogous statements for partially ordered sets and semilattices.     

On Smooth Lattice Polytopes with Small Degree

Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this article, we explore this correspondence to classify smooth lattice polytopes having small degree, extending a classification provided by Dickenstein, Di Rocco, and Piene. We follow their approach of interpreting the degree of a polytope as a geometric invariant of the corresponding polarized variety, and then apply techniques from Adjunction Theory and Mori Theory.     

Lattice Modules over Principal Element Domains

Abstract

This paper obtains a structure theorem for a finitely generated lattice module 𝔐 over a Noetherian principal element domain 𝔏,with a slightly stronger theorem if the lattice module satisfies a hypothesis valid over principal ideal domains. Additionally,we obtain a new characterization of Dedekind lattice domains as multiplicative lattice domains over which there exists a non torsion,principally generated,Noetherian join-principal-element lattice module.     

On Matrix Rings and Subhereditary Radicals

Abstract

We study some one-sided ideals of row bounded and of column bounded matrix rings over free algebras. Obtained results are applied to answer several open problems on subhereditary radicals of associative rings. In particular we show that the right strongly prime radical is not left subhereditary and that the lattice of left (right) subhereditary radicals is not complete.