1,720,974 research outputs found
Lattice Gauge Theory and a Random-Medium Ising Model
No full textWe study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.The work is supported by Ministry of Science and Higher Education of the Russian Federation, agreement N075-15-2019-1619.
For the latter conjecture, there have been suggested a proof by K. Izyurov and A. Magazinov, as well as interesting generalizations by M. Fedorov and I. Novikov (private communication) [16 , 17]. The author is grateful to D. Chelkak, H. Duminil-Copin, M. Khristoforov, S. Melikhov, S. Smirnov for useful discussions
The boundary value problem for discrete analytic functions
No full textThis paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.The author was partially supported by "Dynasty" foundation, by the Simons-IUM fellowship, and by the President of the Russian Federation grant MK-3965.2012.1
Discrete Riemann surfaces: Linear discretization and its convergence
No full textWe develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and discrete Abelian integrals to their continuous counterparts. We also prove a discrete counterpart of the Riemann–Roch theorem. The proofs use energy estimates inspired by electrical networks.The first author was partially supported by the DFG Collaborative Research Center SFB/TR 109 “Discretization in Geometry and Dynamics”. The second author was partially supported by the President of the Russian Federation grant MK-5490.2014.1, by “Dynasty” foundation, and by the Simons–IUM fellowship. Part of the work on this paper was done during the stay of the second author at King Abdullah University of Science and Technology in Saudi Arabia
On approximability by embeddings of cycles in the plane
No full textAbstractWe obtain a criterion for approximability of PL maps S1→R2 by embeddings, analogous to the one proved by Minc for PL maps I→R2.Theorem. Let ϕ:S1→R2 be a PL map, which is simplicial for some triangulation of S1 with k vertices. The map ϕ is approximable by embeddings if and only if for each i=0,…,k the ith derivative ϕ(i) (defined by Minc) neither contains transversal self-intersections nor is the standard winding of degree, ∉{−1,0,1}.We deduce from the Minc result the completeness of the van Kampen obstruction to approximability by embeddings of PL maps I→R2 (Corollary 1.4). We also generalize these criteria to simplicial maps T→S1⊂R2, where T is a graph without vertices of degree >3 (Theorem 1.5)
A surface containing a line and a circle through each point is a quadric
No full textWe prove that a surface in 3-dimensional Euclidean space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point. © 2012 Springer Science+Business Media B.V.The authors were supported in part by President of the Russian Federation grant MK-3965.2012.1 and the program FCP-2012-1.2.2-12-000-1001-7779. The second author was supported in part by "Dynasty" foundation and Simons-IUM fellowship
Discrete field theory: symmetries and conservation laws
Full text linkWe present a general algorithm constructing a discretization of a classical
field theory from a Lagrangian. We prove a new discrete Noether theorem
relating symmetries to conservation laws and an energy conservation theorem not
based on any symmetry. This gives exact conservation laws for several theories,
e.g., lattice electrodynamics and gauge theory. In particular, we construct a
conserved discrete energy-momentum tensor, approximating the continuum one at
least for free fields. The theory is stated in topological terms, such as
coboundary and products of cochains.Comment: 46 pages, 10 figures; exposition improved: more detailed comparison
to the existing literature added, text reordered to minimize forward
reference
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Lattice gauge theory and a random-medium Ising model
Full text linkWe study linearization of lattice gauge theory. Linearized theory
approximates lattice gauge theory in the same manner as the loop O(n)-model
approximates the spin O(n)-model. Under mild assumptions, we show that the
expectation of an observable in linearized Abelian gauge theory coincides with
the expectation in the Ising model with random edge-weights. We find a similar
relation between Yang-Mills theory and 4-state Potts model. For the latter, we
introduce a new observable.Comment: 10 pages, 2 figure
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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