Scaling limit for a drainage network model

We consider the two dimensional version of a drainage network model introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman and Ravishankar.Comment: 15 page

Lattice Gauge Theories and the Heisenberg Antiferromagnetic Chain

We study the strongly coupled 2-flavor lattice Schwinger model and the SU(2)-color QCD_2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin-1/2 chain.Comment: Proceedings LATTICE99 (spin models), 3 page

A stochastic two-stage innovation diffusion model on a lattice

We propose a stochastic model describing a process of awareness, evaluation and decision-making by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0, 1, 2}. In this model 0 stands for ignorants, 1 for aware and 2 for adopters. Aware and adopters inform its nearest ignorant neighbors about a new product innovation at rate lambda. At rate alpha an agent in aware state becomes an adopter due to the influence of adopters neighbors. Finally, aware and adopters forget the information about the new product, thus becoming ignorant, at rate one. Our purpose is to analyze the influence of the parameters on the qualitative behavior of the process. We obtain sufficient conditions under which the innovation diffusion (and adoption) either becomes extinct or propagates through the population with positive probability.Comment: Theorem 2.4 has been improved and some minor changes have been made. To appear in J. Appl. Proba

Testing Closed String Field Theory with Marginal Fields

We study the feasibility of level expansion and test the quartic vertex of closed string field theory by checking the flatness of the potential in marginal directions. The tests, which work out correctly, require the cancellation of two contributions: one from an infinite-level computation with the cubic vertex and the other from a finite-level computation with the quartic vertex. The numerical results suggest that the quartic vertex contributions are comparable or smaller than those of level four fields.Comment: 14 pages, LaTeX. v2: New references to work of Beccaria and Rampino, and Taylor. Improved numerical analysis at the end of section

Field Redefinitions, T-duality and Solutions in Closed String Field Theories

We investigate classical solutions in closed bosonic string field theory and heterotic string field theory that are obtained order by order starting from solutions of the linearized equations of motion, and we discuss the ``field redefinitions'' which relate massless fields in the string field theory side and the low energy effective theory side. Massless components of the string field theory solutions are not corrected and from them we can infer corresponding solutions in the effective theory: the chiral null model and the pp-wave solution with B-field, which have been known to be alpha'-exact. These two sets of solutions in the two sides look slightly different because of the field redefinitions. It turns out that T-duality is a useful tool to determine them: We show that some part of the field redefinitions can be determined by using the correspondence between T-duality rules in the two sides, irrespective of the detail of the interaction terms and the integrating-out procedure. Applying the field redefinitions, we see that the solutions in the effective theory side are reproduced from the string field theory solutions.Comment: LaTeX, 40 pages, no figure v2: minor corrections v3: minor correctio

Homotopy Lie Superalgebra in Yang-Mills Theory

The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.Comment: LaTeX2e, 10 page

Electrochemical synthesis of C-glycosides as non-natural mimetics of biologically active oligosaccharides

Natural oligosaccharides inhibitors of heparanase and selectins are emerging as promising drugs for cancer therapy. As an alternative tool to the natural ones, sulfated tri maltose C-C-linked dimers (alfa,alfa alfa,beta and beta,beta STMCs) were prepared by bromo-maltotriose electroreduction on silver cathode,1 followed by sulfation. The presence of an interglycosidic C-C bond makes STMCs less vulnerable to metabolic processing then their O-analogues. For this reason, STMCs have been studied as drug candidates and inhibitors of carbohydrate processing enzymes. Their activity as inhibitor of Pselectin in vivo and in the attenuation of metastasis both on B16-BL6 melanoma cells and on MC- 38 carcinoma cells2 prompted to the optimization of their synthetic process. Therefore, the electrochemical process for the C-C coupling of the model molecule acetobromoglucose has been investigated by changing various reaction conditions such as solvent and arrangement of the electrolytic cell, aiming at the final scale-up of the reaction

A solution to the 4-tachyon off-shell amplitude in cubic string field theory

We derive an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude in cubic string field theory (CSFT). From such a solution we compute the exact coefficient of the quartic effective action relevant for time dependent solutions and we derive the exact coefficient of the quartic tachyon coupling. The rolling tachyon solution expressed as a series of exponentials $e^t$ is studied both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level truncated coefficients are shown to converge to those derived using the exact string amplitude. The agreement with previous work on the subject, both on the quartic tachyon coupling and on the CSFT rolling tachyon, is an excellent test for the accuracy of our off-shell solution.Comment: 26 pages, 5 figure

Ultrafast Momentum Imaging of Pseudospin-Flip Excitations in Graphene

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photo-excited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization, and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy and in-plane momentum. We first show that the rapidly-established quasi-thermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photo-excited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photo-control experiments and optoelectronic device applications.Comment: 23 pages, 12 figure

Strongly coupled 't Hooft model on the lattice

A lattice strong coupling calculation of the spectrum and chiral condensate of the 't Hooft model is presented. The agreement with the results of the continuum theory is strikingly good even at the fourth order in the strong coupling expansion.Comment: LATTICE99(Spin Models), talk presented by F. Berruto, 3 pages, LaTex, espcrc2.st