57 research outputs found

### Six degree of freedom FORTRAN program, ASTP docking dynamics, users guide

The digital program ASTP Docking Dynamics as outlined is intended to aid the engineer using the program to determine the docking system loads and attendant vehicular motion resulting from docking two vehicles that have an androgynous, six-hydraulic-attenuator, guide ring, docking interface similar to that designed for the Apollo/Soyuz Test Project (ASTP). This program is set up to analyze two different vehicle combinations: the Apollo CSM docking to Soyuz and the shuttle orbiter docking to another orbiter. The subroutine modifies the vehicle control systems to describe one or the other vehicle combinations; the rest of the vehicle characteristics are changed by input data. To date, the program has been used to predict and correlate ASTP docking loads and performance with docking test program results from dynamic testing. The program modified for use on IBM 360 computers. Parts of the original docking system equations in the areas of hydraulic damping and capture latches are modified to better describe the detail design of the ASTP docking system

### Correlation function for a periodic box-ball system

We investigate correlation functions in a periodic box-ball system. For the
two point functions of short distance, we give explicit formulae obtained by
combinatorial methods. We give expressions for general N-point functions in
terms of ultradiscrete theta functions.Comment: 13 pages, 2 figures, submitted to J. Phys. A: Math. Theo

### Computing Tropical Varieties

The tropical variety of a $d$-dimensional prime ideal in a polynomial ring
with complex coefficients is a pure $d$-dimensional polyhedral fan. This fan is
shown to be connected in codimension one. We present algorithmic tools for
computing the tropical variety, and we discuss our implementation of these
tools in the Gr\"obner fan software \texttt{Gfan}. Every ideal is shown to have
a finite tropical basis, and a sharp lower bound is given for the size of a
tropical basis for an ideal of linear forms.Comment: 22 pages, 2 figure

### Tropical surface singularities

In this paper, we study tropicalisations of singular surfaces in toric
threefolds. We completely classify singular tropical surfaces of
maximal-dimensional type, show that they can generically have only finitely
many singular points, and describe all possible locations of singular points.
More precisely, we show that singular points must be either vertices, or
generalized midpoints and baricenters of certain faces of singular tropical
surfaces, and, in some cases, there may be additional metric restrictions to
faces of singular tropical surfaces.Comment: A gap in the classification was closed. 37 pages, 29 figure

### A Non-Algebraic Patchwork

Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle
more flexible than Viro's original algebraic one. It was natural to wonder if
the former method allows one to construct non-algebraic objects. In this paper
we construct the first examples of patchworked real pseudoholomorphic curves in
$\Sigma_n$ whose position with respect to the pencil of lines cannot be
realised by any homologous real algebraic curve.Comment: 6 pages, 1 figur

### Singular Tropical Hypersurfaces

We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal intersection points of planar tropical curves

### Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

We study various aspects of the matrix models calculating free energies and
Wilson loop observables in supersymmetric Chern-Simons-matter theories on the
three-sphere. We first develop techniques to extract strong coupling results
directly from the spectral curve describing the large N master field. We show
that the strong coupling limit of the gauge theory corresponds to the so-called
tropical limit of the spectral curve. In this limit, the curve degenerates to a
planar graph, and matrix model calculations reduce to elementary line integrals
along the graph. As an important physical application of these tropical
techniques, we study N=3 theories with fundamental matter, both in the quenched
and in the unquenched regimes. We calculate the exact spectral curve in the
Veneziano limit, and we evaluate the planar free energy and Wilson loop
observables at strong coupling by using tropical geometry. The results are in
agreement with the predictions of the AdS duals involving tri-Sasakian
manifoldsComment: 32 pages, 7 figures. v2: small corrections, added an Appendix on the
relation with the approach of 1011.5487. v3: further corrections and
clarifications, final version to appear in JHE

### Intersecting Solitons, Amoeba and Tropical Geometry

We study generic intersection (or web) of vortices with instantons inside,
which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1
supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1}
\times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the
case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can
be beautifully understood in a mathematical framework of amoeba and tropical
geometry, and we propose a dictionary relating solitons and gauge theory to
amoeba and tropical geometry. A projective shape of vortex sheets is described
by the amoeba. Vortex charge density is uniformly distributed among vortex
sheets, and negative contribution to instanton charge density is understood as
the complex Monge-Ampere measure with respect to a plurisubharmonic function on
(C^\ast)^2. The Wilson loops in T^2 are related with derivatives of the Ronkin
function. The general form of the Kahler potential and the asymptotic metric of
the moduli space of a vortex loop are obtained as a by-product. Our discussion
works generally in non-Abelian gauge theories, which suggests a non-Abelian
generalization of the amoeba and tropical geometry.Comment: 39 pages, 11 figure

### Stability data, irregular connections and tropical curves

We study a class of meromorphic connections nabla(Z) on P^1, parametrised by the central charge Z of a stability condition, with values in a Lie algebra of formal vector fields on a torus. Their definition is motivated by the work of Gaiotto, Moore and Neitzke on wall-crossing and three-dimensional field theories. Our main results concern two limits of the families nabla(Z) as we rescale the central charge Z to RZ. In the R to 0 ``conformal limit'' we recover a version of the connections introduced by Bridgeland and Toledano Laredo (and so the Joyce holomorphic generating functions for enumerative invariants), although with a different construction yielding new explicit formulae. In the R to infty ``large complex structure" limit the connections nabla(Z) make contact with the Gross-Pandharipande-Siebert approach to wall-crossing based on tropical geometry. Their flat sections display tropical behaviour, and also encode certain tropical/relative Gromov-Witten invariants

### Consistency and derangements in brane tilings

journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Consistency and derangements in brane tilings copyright_information: © 2016 IOP Publishing Ltd date_received: 2016-03-22 date_accepted: 2016-07-06 date_epub: 2016-07-29journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Consistency and derangements in brane tilings copyright_information: © 2016 IOP Publishing Ltd date_received: 2016-03-22 date_accepted: 2016-07-06 date_epub: 2016-07-29journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Consistency and derangements in brane tilings copyright_information: © 2016 IOP Publishing Ltd date_received: 2016-03-22 date_accepted: 2016-07-06 date_epub: 2016-07-2

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