8,256 research outputs found
MHV amplitudes at strong coupling and linearized TBA equations
The maximally helicity violating (MHV) amplitudes of super
Yang-Mills theory at strong coupling are obtained by solving auxiliary
thermodynamic Bethe ansatz (TBA) integral equations. We consider a limit where
the TBA equations are linearized for large chemical potentials and masses
therein. By solving the linearized equations, we derive analytic expansions of
the 6-point MHV amplitudes in terms of the ratio of the chemical potential
and the mass . The expansions are valid up to corrections exponentially
small in or inversely proportional to powers of . The analytic
expansions describe the amplitudes for small conformal cross-ratios of the
particle momenta in a standard basis, and interpolate the amplitudes with equal
cross-ratios and those in soft/collinear limits. The leading power corrections
are also obtained analytically. We compare the 6-point rescaled remainder
functions at strong coupling and at 2 loops for the above kinematics. They are
rather different, in contrast to other kinematic regions discussed in the
literature where they are found to be similar to each other.Comment: 41 pages, 9 figures; (v2) a reference added, typos corrected, minor
revision
On the Oß-hull of a planar point set
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We study the Oß-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle ß. Given a set P of n points in the plane, we show how to maintain the Oß-hull of P while ß runs from 0 to p in T(n log n) time and O(n) space. With the same complexity, we also find the values of ß that maximize the area and the perimeter of the Oß-hull and, furthermore, we find the value of ß achieving the best fitting of the point set P with a two-joint chain of alternate interior angle ß.Peer ReviewedPostprint (author's final draft
Elementary approach to closed billiard trajectories in asymmetric normed spaces
We apply the technique of K\'aroly Bezdek and Daniel Bezdek to study billiard
trajectories in convex bodies, when the length is measured with a (possibly
asymmetric) norm. We prove a lower bound for the length of the shortest closed
billiard trajectory, related to the non-symmetric Mahler problem. With this
technique we are able to give short and elementary proofs to some known
results.Comment: 10 figures added. The title change
Embedded Implicit Stand-ins for Animated Meshes: a Case of Hybrid Modelling
In this paper we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. This approach is used to model the interaction between an animated mesh object and a viscoelastic substance, normally modelled in implicit form. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented
- …