Algebraic Aspects of Abelian Sandpile Models

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G, and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of toppling matrix. We construct scalar functions, linear in height variables of the pile, that are invariant toppling at any site. These invariants provide convenient coordinates to label the recurrent configurations of the sandpile. For an L X L square lattice, we show that g = L. In this case, we observe that the system has nontrivial symmetries coming from the action of the cyclotomic Galois group of the (2L+2)th roots of unity which operates on the set of eigenvalues of the toppling matrix. These eigenvalues are algebraic integers, whose product is the order |G|. With the help of this Galois group, we obtain an explicit factorizaration of |G|. We also use it to define other simpler, though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3

Biocomposites of poly(lactic acid) and lactic acid oligomer-grafted bacterial cellulose: It's preparation and characterization

This work demonstrates the synthesis of lactic acid oligomer-grafted-untreated bacterial cellulose (OLLA-g-BC) by in situ condensation polymerization which increased compatibilization between hydrophobic poly(lactic acid) (PLA) and hydrophilic BC, thus enhancing various properties of PLA-based bionanocomposites, indispensable for stringent food-packaging applications. During the synthesis of OLLA-g-BC, hydrophilic BC is converted into hydrophobic due to structural grafting of OLLA chains with BC molecules. Subsequently, bionanocomposites films are fabricated using solution casting technique and characterized for structural, thermal, mechanical, optical, and gas-barrier properties. Morphological images showed uniform dispersion of BC nanospheres in the PLA matrix, which shows strong filler–matrix interaction. The degradation temperatures for bionanocomposites films were above PLA processing temperature indicating that bionanocomposite processing can be industrially viable. Bionanocomposites films displayed decrease in glass transition (T g ) and ~20% improvement in elongation with 10 wt % fillers indicating towards plasticization of PLA. PLA/OLLA-g-BC films showed a slight reduction in optical transparency but had excellent UV-blocking characteristics. Moreover, dispersed BC act as blocking agents within PLA matrix, reducing the diffusion through the bionanocomposite films which showed ~40% improvement in water-vapor barrier by 5 wt % filler addition, which is significant. The reduced T g , improved elongation combined with improved hydrophobicity and water-vapor barrier make them suitable candidate for flexible food-packaging applications. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47903. © 2019 Wiley Periodicals, Inc

Rolling tachyon solution of two-dimensional string theory

We consider a classical (string) field theory of $c=1$ matrix model which was developed earlier in hep-th/9207011 and subsequent papers. This is a noncommutative field theory where the noncommutativity parameter is the string coupling $g_s$. We construct a classical solution of this field theory and show that it describes the complete time history of the recently found rolling tachyon on an unstable D0 brane.Comment: 19 pages, 2 figures, minor changes in text and additional references, correction of decay time (version to appear in JHEP.

Conservation Laws and Integrability of a One-dimensional Model of Diffusing Dimers

We study a model of assisted diffusion of hard-core particles on a line. The model shows strongly ergodicity breaking : configuration space breaks up into an exponentially large number of disconnected sectors. We determine this sector-decomposion exactly. Within each sector the model is reducible to the simple exclusion process, and is thus equivalent to the Heisenberg model and is fully integrable. We discuss additional symmetries of the equivalent quantum Hamiltonian which relate observables in different sectors. In some sectors, the long-time decay of correlation functions is qualitatively different from that of the simple exclusion process. These decays in different sectors are deduced from an exact mapping to a model of the diffusion of hard-core random walkers with conserved spins, and are also verified numerically. We also discuss some implications of the existence of an infinity of conservation laws for a hydrodynamic description.Comment: 39 pages, with 5 eps figures, to appear in J. Stat. Phys. (March 1997

Magnetic structure of EuFe2As2 determined by single crystal neutron diffraction

Among various parent compounds of iron pnictide superconductors, EuFe2As2 stands out due to the presence of both spin density wave of Fe and antiferromagnetic ordering (AFM) of the localized Eu2+ moment. Single crystal neutron diffraction studies have been carried out to determine the magnetic structure of this compound and to investigate the coupling of two magnetic sublattices. Long range AFM ordering of Fe and Eu spins was observed below 190 K and 19 K, respectively. The ordering of Fe2+ moments is associated with the wave vector k = (1,0,1) and it takes place at the same temperature as the tetragonal to orthorhombic structural phase transition, which indicates the strong coupling between structural and magnetic components. The ordering of Eu moment is associated with the wave vector k = (0,0,1). While both Fe and Eu spins are aligned along the long a axis as experimentally determined, our studies suggest a weak coupling between the Fe and Eu magnetism.Comment: 7 pages, 7 figure

Exact solutions for a mean-field Abelian sandpile

We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe

Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions

We show that in the loop-erased random walk problem, the exponent characterizing probability distribution of areas of erased loops is superuniversal. In d-dimensions, the probability that the erased loop has an area A varies as A^{-2} for large A, independent of d, for 2 <= d <= 4. We estimate the exponents characterizing the distribution of perimeters and areas of erased loops in d = 2 and 3 by large-scale Monte Carlo simulations. Our estimate of the fractal dimension z in two-dimensions is consistent with the known exact value 5/4. In three-dimensions, we get z = 1.6183 +- 0.0004. The exponent for the distribution of durations of avalanche in the three-dimensional abelian sandpile model is determined from this by using scaling relations.Comment: 25 pages, 1 table, 8 figure