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A Morozov - One of the best experts on this subject based on the ideXlab platform.

  • Boundary ring a way to construct approximate ng solutions with Polygon Boundary conditions i zn symmetric configurations
    Nuclear Physics, 2009
    Co-Authors: H Itoyama, A Mironov, A Morozov
    Abstract:

    Abstract We describe an algebro-geometric construction of Polygon-bounded minimal surfaces in AdS 5 , based on the consideration of what we call the “Boundary ring” of polynomials. The first non-trivial example of solutions to the Nambu–Goto (NG) equations for Z 6 -symmetric hexagon is considered in some detail. Solutions are represented as power series, of which only the first terms are evaluated. The NG equations leave a number of free parameters (a free function). Boundary conditions, which fix the free parameters, are imposed on truncated series. A better use, albeit being exotic to theory of PDE, of the Boundary ring is suggested as well. It is still unclear if explicit analytic formulas can be found in this way, but even approximate solutions, obtained by truncation of power series, can be sufficient to investigate the Alday–Maldacena—BDS/BHT version of the string/gauge duality.

  • Boundary ring or a way to construct approximate ng solutions with Polygon Boundary conditions ii Polygons which admit an inscribed circle
    arXiv: High Energy Physics - Theory, 2007
    Co-Authors: H Itoyama, A Morozov
    Abstract:

    We further develop the formalism of arXiv:0712.0159 for approximate solution of Nambu-Goto (NG) equations with Polygon conditions in AdS backgrounds, needed in modern studies of the string/gauge duality. Inscribed circle condition is preserved, which leaves only one unknown function y_0(y_1,y_2) to solve for, what considerably simplifies our presentation. The problem is to find a delicate balance -- if not exact match -- between two different structures: NG equation -- a non-linear deformation of Laplace equation with solutions non-linearly deviating from holomorphic functions, -- and the Boundary ring, associated with Polygons made from null segments in Minkovski space. We provide more details about the theory of these structures and suggest an extended class of functions to be used at the next stage of Alday-Maldacena program: evaluation of regularized NG actions.

H Itoyama - One of the best experts on this subject based on the ideXlab platform.

  • Boundary ring a way to construct approximate ng solutions with Polygon Boundary conditions i zn symmetric configurations
    Nuclear Physics, 2009
    Co-Authors: H Itoyama, A Mironov, A Morozov
    Abstract:

    Abstract We describe an algebro-geometric construction of Polygon-bounded minimal surfaces in AdS 5 , based on the consideration of what we call the “Boundary ring” of polynomials. The first non-trivial example of solutions to the Nambu–Goto (NG) equations for Z 6 -symmetric hexagon is considered in some detail. Solutions are represented as power series, of which only the first terms are evaluated. The NG equations leave a number of free parameters (a free function). Boundary conditions, which fix the free parameters, are imposed on truncated series. A better use, albeit being exotic to theory of PDE, of the Boundary ring is suggested as well. It is still unclear if explicit analytic formulas can be found in this way, but even approximate solutions, obtained by truncation of power series, can be sufficient to investigate the Alday–Maldacena—BDS/BHT version of the string/gauge duality.

  • Boundary ring or a way to construct approximate ng solutions with Polygon Boundary conditions ii Polygons which admit an inscribed circle
    arXiv: High Energy Physics - Theory, 2007
    Co-Authors: H Itoyama, A Morozov
    Abstract:

    We further develop the formalism of arXiv:0712.0159 for approximate solution of Nambu-Goto (NG) equations with Polygon conditions in AdS backgrounds, needed in modern studies of the string/gauge duality. Inscribed circle condition is preserved, which leaves only one unknown function y_0(y_1,y_2) to solve for, what considerably simplifies our presentation. The problem is to find a delicate balance -- if not exact match -- between two different structures: NG equation -- a non-linear deformation of Laplace equation with solutions non-linearly deviating from holomorphic functions, -- and the Boundary ring, associated with Polygons made from null segments in Minkovski space. We provide more details about the theory of these structures and suggest an extended class of functions to be used at the next stage of Alday-Maldacena program: evaluation of regularized NG actions.

A Mironov - One of the best experts on this subject based on the ideXlab platform.

  • Boundary ring a way to construct approximate ng solutions with Polygon Boundary conditions i zn symmetric configurations
    Nuclear Physics, 2009
    Co-Authors: H Itoyama, A Mironov, A Morozov
    Abstract:

    Abstract We describe an algebro-geometric construction of Polygon-bounded minimal surfaces in AdS 5 , based on the consideration of what we call the “Boundary ring” of polynomials. The first non-trivial example of solutions to the Nambu–Goto (NG) equations for Z 6 -symmetric hexagon is considered in some detail. Solutions are represented as power series, of which only the first terms are evaluated. The NG equations leave a number of free parameters (a free function). Boundary conditions, which fix the free parameters, are imposed on truncated series. A better use, albeit being exotic to theory of PDE, of the Boundary ring is suggested as well. It is still unclear if explicit analytic formulas can be found in this way, but even approximate solutions, obtained by truncation of power series, can be sufficient to investigate the Alday–Maldacena—BDS/BHT version of the string/gauge duality.

Xing Yi-lan - One of the best experts on this subject based on the ideXlab platform.

Subhash Suri - One of the best experts on this subject based on the ideXlab platform.

  • A Pedestrian Approach to Ray Shooting
    Journal of Algorithms, 1995
    Co-Authors: John Hershberger, Subhash Suri
    Abstract:

    We propose a very simple ray-shooting algorithm, whose only data structure is a triangulation. The query algorithm, after locating the triangle containing the origin of the ray, walks along the ray, advancing from one triangle to a neighboring one until the Polygon Boundary is reached. The key result of the paper is a Steiner triangulation of a simple Polygon with the property that a ray can intersect at most O(log n) triangles before reaching the Polygon Boundary. We are able to compute such a triangulation in linear sequential time, or in O(log n) parallel time using O(n/log n) processors. This gives a simple, yet optimal, ray-shooting algorithm for a simple Polygon. Using a well-known technique, we can extend our triangulation procedure to a multiconnected Polygon with k components and n vertices, so that a ray intersects at most O(?k log n) triangles.

  • SODA - A pedestrian approach to ray shooting: shoot a ray, take a walk
    1993
    Co-Authors: John Hershberger, Subhash Suri
    Abstract:

    We propose a very simple ray-shooting algorithm, whose only data structure is a triangulation. The query algorithm, after locating the triangle containing the origin of the ray, walks along the ray, advancing from one triangle to a neighboring one until the Polygon Boundary is reached. The key result of the paper is a Steiner triangulation of a simple Polygon with the property that a ray can intersect at most O(log n) triangles before reaching the Polygon Boundary. We are able to compute such a triangulation in linear sequential time, or in O(log n) parallel time using O(n/log n) processors. This gives a simple, yet optimal, ray-shooting algorithm for a simple Polygon. Using a well-known technique, we can extend our triangulation procedure to a multiconnected Polygon with k components and n vertices, so that a ray intersects at most O(√κ log n) triangles. © 1995 Academic Press, Inc.