Related papers: Universal $\alpha$-elasticity of generalized Moufa…
Dielectric measurements on molecular liquids just above the glass transition indicate that alpha relaxation is characterized by a generic high-frequency loss varying as $\omega^{-1/2}$, whereas deviations from this come from one or more…
In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot…
We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector…
In this work, we provide a q-generalization of flexible algebras and related bialgebraic structures, including center-symmetric (also called antiflexible) algebras, and their bialgebras. Their basic properties are derived and discussed.…
We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to an extensional force We show that with an increase in the applied force…
An A-loop is a loop in which every inner mapping is an automorphism. We settle a problem which had been open since 1956 by showing that every diassociative A-loop is Moufang.
Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at…
In math.GR/0510298, we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups.…
One of the most important scaling laws of time dependent fracture is Basquin's law of fatigue, namely, that the lifetime of the system increases as a power law with decreasing external load amplitude, $t_f\sim \sigma_0^{-\alpha}$, where the…
We present a construction of gauge theory which its structure group is not a Lie group, but a Moufang loop which is essentially non-associative. As an example of non-associative algebra, we take octonions with norm one as a Moufang loop,…
The existence of a fundamental length scale in Nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg…
The notion of Moufang set was introduced by Jacques Tits in \cite{Tits92}. We recall briefly the well-established definition and a construction which, under certain conditions, yields a Moufang set. We show that these conditions can be…
We establish conditions under which the universal and reduced norms coincide for a Fell bundle over a groupoid. Specifically, we prove that the full and reduced C*-algebras of any Fell bundle over a measurewise amenable groupoid coincide,…
We find that the frequency spectra of layered phononic and photonic composites admit a universal struc- ture, independent of the geometry of the periodic-cell and the specific physical properties. We show that this representation extends to…
Given a partial action $\alpha=(A_g,\alpha_g)_{g\in \mathcal{G}}$ of a connected groupoid $\mathcal{G}$ on a ring $A$ and an object $x$ of $\mathcal{G}$, the isotropy group $\mathcal{G}(x)$ acts partially on the ideal $A_x$ of $A$ by the…
We give a construction of a universal average of Lie algebra elements whose exponentiation gives (when there is an associated Lie group) a totally symmetric geometric mean of Lie group elements (sufficiently closed to the identity) with the…
We consider the asymmetric version of the Popkov-Sch\"{u}tz two-lane lattice gas with general jump rates, subject to the stationary measure being of product form. This still leaves five free parameters. At density 1/2 the eigenvalues of the…
Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. In this…
We consider generalized Wigner ensembles and general beta-ensembles with analytic potentials for any beta larger than 1. The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk…
We review our recent proposal for a universal description of generic single-component viscoelastic systems with a single relaxation time. Foliation preserving diffeomorphisms are introduced as an underlying symmetry which naturally…