Heat conduction in deformable Frenkel-Kontorova lattices: thermal conductivity and negative differential thermal resistance

Heat conduction through the Frenkel-Kontorova (FK) lattices is numerically investigated in the presence of a deformable substrate potential. It is found that the deformation of the substrate potential has a strong influence on heat conduction. The thermal conductivity as a function of the shape parameter is nonmonotonic. The deformation can enhance thermal conductivity greatly and there exists an optimal deformable value at which thermal conductivity takes its maximum. Remarkably, we also find that the deformation can facilitate the appearance of the negative differential thermal resistance (NDTR).Comment: 15 pages, 7 figure

Boundary Friction on Molecular Lubricants: Rolling Mode?

A theoretical model is proposed for low temperature friction between two smooth rigid solid surfaces separated by lubricant molecules, admitting their deformations and rotations. Appearance of different modes of energy dissipation (by ''rocking'' or ''rolling'' of lubricants) at slow relative displacement of the surfaces is shown to be accompanied by the stick-and-slip features and reveals a non-monotonic (mean) friction force {\it vs} external loadComment: revtex4, 4 pages, 5 figure

(In)commensurability, scaling and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite

The scaling of friction with the contact size $A$ and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are assumed to be stiff, but not completely rigid. Commensurate and incommensurate configurations are identified systematically. It is shown that three distinct friction branches coexist, an incommensurate one that does not scale with the contact size ($A^0$) and two commensurate ones which scale differently (with $A^{1/2}$ and $A$) and are associated with various combinations of commensurate and incommensurate lattice parameters and orientations. This coexistence is a direct consequence of the two-dimensional nature of the contact layer, and such multiplicity exists in all geometries consisting of regular lattices. To demonstrate this, the procedure is repeated for rectangular geometry. The scaling of irregularly shaped crystals is also considered, and again three branches are found ($A^{1/4}, A^{3/4}, A$). Based on the scaling properties, a quantity is defined which can be used to classify commensurability in infinite as well as finite contacts. Finally, the consequences for friction experiments on gold nanocrystals on graphite are discussed

Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad).Comment: 42 page

Vertex operator algebras and operads

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal to $0$, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation shows that the rich geometric structure revealed in the study of conformal field theory and the rich algebraic structure of the theory of vertex operator algebras share a precise common foundation in basic operations associated with a certain kind of (two-dimensional) ``complex'' geometric object, in the sense in which classical algebraic structures (groups, algebras, Lie algebras and the like) are always implicitly based on (one-dimensional) ``real'' geometric objects. In effect, the standard analogy between point-particle theory and string theory is being shown to manifest itself at a more fundamental mathematical level.Comment: 16 pages. Only the definitions of "partial operad" and of "rescaling group" have been improve

The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

The 3-graviton vertex function in thermal quantum gravity

The high temperature limit of the 3-graviton vertex function is studied in thermal quantum gravity, to one loop order. The leading ($T^4$) contributions arising from internal gravitons are calculated and shown to be twice the ones associated with internal scalar particles, in correspondence with the two helicity states of the graviton. The gauge invariance of this result follows in consequence of the Ward and Weyl identities obeyed by the thermal loops, which are verified explicitly.Comment: 19 pages, plain TeX, IFUSP/P-100

Direct Separation of Short Range Order in Intermixed Nanocrystalline and Amorphous Phases

Diffraction anomalous fine-structure (DAFS) and extended x-ray absorption fine-structure (EXAFS) measurements were combined to determine short range order (SRO) about a single atomic type in a sample of mixed amorphous and nanocrystalline phases of germanium. EXAFS yields information about the SRO of all Ge atoms in the sample, while DAFS determines the SRO of only the ordered fraction. We determine that the first-shell distance distribution is bimodal; the nanocrystalline distance is the same as the bulk crystal, to within 0.01(2)   Å, but the mean amorphous Ge-Ge bond length is expanded by 0.076(19)   Å. This approach can be applied to many systems of mixed amorphous and nanocrystalline phases

Z-graded weak modules and regularity

It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.Comment: 9 page

Theory of reversible and nonreversible cracks in solids

The Griffith crack theory is reviewed and certain shortcomings of this theory are discussed. A new description for the shape of a crack is given which takes into account the atomic structure of material. Through consideration of the total energy of the system and the shape of the crack, expressions for crack behavior are derived which are considered to remedy the defects of the Griffith theory