Efficient Computation of Invariant Tori in Volume-Preserving Maps

In this paper we implement a numerical algorithm to compute codimension-one tori in three-dimensional, volume-preserving maps. A torus is defined by its conjugacy to rigid rotation, which is in turn given by its Fourier series. The algorithm employs a quasi-Newton scheme to find the Fourier coefficients of a truncation of the series. This technique is based upon the theory developed in the accompanying article by Blass and de la Llave. It is guaranteed to converge assuming the torus exists, the initial estimate is suitably close, and the map satisfies certain nondegeneracy conditions. We demonstrate that the growth of the largest singular value of the derivative of the conjugacy predicts the threshold for the destruction of the torus. We use these singular values to examine the mechanics of the breakup of the tori, making comparisons to Aubry-Mather and anti-integrability theory when possible

Multiple phase transitions in an agent-based evolutionary model with neutral fitness

Null models are crucial for understanding evolutionary processes such as speciation and adaptive radiation. We analyse an agent-based null model, considering a case without selection—neutral evolution—in which organisms are defined only by phenotype. Universal dynamics has previously been demonstrated in a related model on a neutral fitness landscape, showing that this system belongs to the directed percolation (DP) universality class. The traditional null condition of neutral fitness (where fitness is defined as the number of offspring each organism produces) is extended here to include equal probability of death among organisms. We identify two types of phase transition: (i) a non-equilibrium DP transition through generational time (i.e. survival), and (ii) an equilibrium ordinary percolation transition through the phenotype space (based on links between mating organisms). Owing to the dynamical rules of the DP reaction–diffusion process, organisms can only sparsely fill the phenotype space, resulting in significant phenotypic diversity within a cluster of mating organisms. This highlights the necessity of understanding hierarchical evolutionary relationships, rather than merely developing taxonomies based on phenotypic similarity, in order to develop models that can explain phylogenetic patterns found in the fossil record or to make hypotheses for the incomplete fossil record of deep time

Enhanced di-Higgs Production through Light Colored Scalars

We demonstrate enhanced di-Higgs production at the LHC in the presence of modifications of the effective couplings of Higgs to gluons from new, light, colored scalars. While our results apply to an arbitrary set of colored scalars, we illustrate the effects with a real color octet scalar -- a simple, experimentally viable model involving a light (~125-300 GeV) colored scalar. Given the recent LHC results, we consider two distinct scenarios: First, if the Higgs is indeed near 125 GeV, we show that the di-Higgs cross section could be up to nearly one thousand times the Standard Model rate for particular octet couplings and masses. This is potentially observable in \emph{single} Higgs production modes, such as $pp \to h h \to \gamma\gamma b\bar{b}$ as well as $pp \to h h \to \tau^+\tau^- b\bar{b}$ where a small fraction of the $\gamma\gamma$ or $\tau^+\tau^-$ events near the putative Higgs invariant mass peak contain also a $b\bar{b}$ resonance consistent with the Higgs mass. Second, if the Higgs is not at 125 GeV (and what the LHC has observed is an impostor), we show that the same parameter region where singly-produced Higgs production can be suppressed below current LHC limits, for a heavier Higgs mass, also simultaneously predicts substantially enhanced di-Higgs production. We point out several characteristic signals of di-Higgs production with a heavier Higgs boson, such as $pp \to hh \to W^+W^-W^+W^-$, which could use same-sign dileptons or trileptons plus missing energy to uncover evidence.Comment: 13 pages, 8 figure