On the sensitivity of the SR decomposition

AbstractFirst-order componentwise and normwise perturbation bounds for the SR decomposition are presented. The new normwise bounds are at least as good as previously known results. In particular, for the R factor, the normwise bound can be significantly tighter than the previous result

A symplectic acceleration method for the solution of the algebraic riccati equation on a parallel computer

AbstractWe give a cubic acceleration method for improving the current symplectic Jacobi-like algorithm for computing the Hamiltonian-Schur decomposition of a Hamiltonian matrix and finding the positive semidefinite solution of the Riccati equation. The acceleration method can speed up the rate of convergence at the end of the symplectic Jacobi-like process when the norm of the current strictly J-lower triangle has become sufficiently small; it has high parallelism and takes O(n) computational time when implemented on a mesh-connected n × n array processor system. A quantitative analysis of convergence and numerical comparisons of one Jacobi sweep versus one correction step are presented

Lyapunov Mode Dynamics in Hard-Disk Systems

The tangent dynamics of the Lyapunov modes and their dynamics as generated numerically - {\it the numerical dynamics} - is considered. We present a new phenomenological description of the numerical dynamical structure that accurately reproduces the experimental data for the quasi-one-dimensional hard-disk system, and shows that the Lyapunov mode numerical dynamics is linear and separate from the rest of the tangent space. Moreover, we propose a new, detailed structure for the Lyapunov mode tangent dynamics, which implies that the Lyapunov modes have well-defined (in)stability in either direction of time. We test this tangent dynamics and its derivative properties numerically with partial success. The phenomenological description involves a time-modal linear combination of all other Lyapunov modes on the same polarization branch and our proposed Lyapunov mode tangent dynamics is based upon the form of the tangent dynamics for the zero modes

Minimal left-right symmetric intersecting D-brane model

We investigate left-right symmetric extensions of the standard model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. The left-handed and right-handed fermions transform as doublets under Sp(1)_L and Sp(1)_R, and so their masses must be generated by the introduction of Higgs fields in a bi-fundamental (2,2) representation under the two Sp(1) gauge groups. For such D-brane configurations the left-right symmetry must be broken by Higgs fields in the doublet representation of Sp(1)_R and therefore Majorana mass terms are suppressed by some higher physics scale. The left-handed and right-handed neutrinos pair up to form Dirac fermions which control the decay widths of the right-handed W' boson to yield comparable branching fractions into dilepton and dijets channels. Using the most recent searches at LHC13 Run II with 2016 data we constrain the (g_R, m_{W'}) parameter space. Our analysis indicates that independent of the coupling strength g_R, gauge bosons with masses m_{W'} \agt 3.5~{\rm TeV} are not ruled out. As the LHC is just beginning to probe the TeV-scale, significant room for W' discovery remains.Comment: To be published in PR