Chaos in a modified Henon-Heiles system describing geodesics in gravitational waves

A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms in the structural function. It is shown that, for energies above a certain value, the motion is chaotic in the sense that the boundaries separating the basins of possible escapes become fractal. Similarities and differences with the standard Henon-Heiles and the monkey saddle systems are discussed. The box-counting dimension of the basin boundaries is also calculated.Comment: 11 pages, 7 figures, LaTeX. To appear in Phys. Lett.

Optimum Monte Carlo Simulations: Some Exact Results

We obtain exact results for the acceptance ratio and mean squared displacement in Monte Carlo simulations of the simple harmonic oscillator in $D$ dimensions. When the trial displacement is made uniformly in the radius, we demonstrate that the results are independent of the dimensionality of the space. We also study the dynamics of the process via a spectral analysis and we obtain an accurate description for the relaxation time.Comment: 17 pages, 8 figures. submitted to J. Phys.

Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium

The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The problem can be solved either under some non-resonance hypotheses on the spectrum of the linear part or if the non-linear term is assumed to be (slowly) decaying in time. This paper "completes" a pioneering work of Pustil'nikov in which, despite under weaker non-resonance hypotheses, the nonlinearity is required to be asymptotically autonomous. The result is obtained as a consequence of the existence of a strong normal form for a suitable class of real-analytic Hamiltonians with non-autonomous perturbations.Comment: 10 page

Texture and shape of two-dimensional domains of nematic liquid crystal

We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios, and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted regime, where the drop is nearly circular, the director field bipolar and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.Comment: 12 pages, 10 figure

Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence

The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists of the possibility to choose an arbitrarily small decaying coefficient, consistently with the perturbation size.Comment: Several corrections in the proof with respect to the previous version. Main statement unchange

Neurospora from natural populations: Population genomics insights into the Life history of a model microbial Eukaryote

The ascomycete filamentous fungus Neurospora crassa played a historic role in experimental biology and became a model system for genetic research. Stimulated by a systematic effort to collect wild strains initiated by Stanford geneticist David Perkins, the genus Neurospora has also become a basic model for the study of evolutionary processes, speciation, and population biology. In this chapter, we will first trace the history that brought Neurospora into the era of population genomics. We will then cover the major contributions of population genomic investigations using Neurospora to our understanding of microbial biogeography and speciation, and review recent work using population genomics and genome-wide association mapping that illustrates the unique potential of Neurospora as a model for identifying the genetic basis of (potentially adaptive) phenotypes in filamentous fungi. The advent of population genomics has contributed to firmly establish Neurospora as a complete model system and we hope our review will entice biologists to include Neurospora in their research

Genetic Architecture of a Reinforced, Postmating, Reproductive Isolation Barrier between Neurospora Species Indicates Evolution via Natural Selection

A role for natural selection in reinforcing premating barriers is recognized, but selection for reinforcement of postmating barriers remains controversial. Organisms lacking evolvable premating barriers can theoretically reinforce postmating isolation, but only under restrictive conditions: parental investment in hybrid progeny must inhibit subsequent reproduction, and selected postmating barriers must restore parents' capacity to reproduce successfully. We show that reinforced postmating isolation markedly increases maternal fitness in the fungus Neurospora crassa, and we detect the evolutionary genetic signature of natural selection by quantitative trait locus (QTL) analysis of the reinforced barrier. Hybrid progeny of N. crassa and N. intermedia are highly inviable. Fertilization by local N. intermedia results in early abortion of hybrid fruitbodies, and we show that abortion is adaptive because only aborted maternal colonies remain fully receptive to future reproduction. In the first QTL analysis of postmating reinforcement in microbial eukaryotes, we identify 11 loci for abortive hybrid fruitbody development, including three major QTLs that together explain 30% of trait variance. One of the major QTLs and six QTLs of lesser effect are found on the mating-type determining chromosome of Neurospora. Several reinforcement QTLs are flanked by genetic markers showing either segregation distortion or non-random associations with alleles at other loci in a cross between N. crassa of different clades, suggesting that the loci also are associated with local effects on same-species reproduction. Statistical analysis of the allelic effects distribution for abortive hybrid fruitbody development indicates its evolution occurred under positive selection. Our results strongly support a role for natural selection in the evolution of reinforced postmating isolation in N. crassa

The Foundation Supernova Survey: Measuring Cosmological Parameters with Supernovae from a Single Telescope

Measurements of the dark energy equation-of-state parameter, $w$, have been limited by uncertainty in the selection effects and photometric calibration of $z<0.1$ Type Ia supernovae (SNe Ia). The Foundation Supernova Survey is designed to lower these uncertainties by creating a new sample of $z<0.1$ SNe Ia observed on the Pan-STARRS system. Here, we combine the Foundation sample with SNe from the Pan-STARRS Medium Deep Survey and measure cosmological parameters with 1,338 SNe from a single telescope and a single, well-calibrated photometric system. For the first time, both the low-$z$ and high-$z$ data are predominantly discovered by surveys that do not target pre-selected galaxies, reducing selection bias uncertainties. The $z>0.1$ data include 875 SNe without spectroscopic classifications and we show that we can robustly marginalize over CC SN contamination. We measure Foundation Hubble residuals to be fainter than the pre-existing low-$z$ Hubble residuals by $0.046 \pm 0.027$ mag (stat+sys). By combining the SN Ia data with cosmic microwave background constraints, we find $w=-0.938 \pm 0.053$, consistent with $\Lambda$CDM. With 463 spectroscopically classified SNe Ia alone, we measure $w=-0.933\pm0.061$. Using the more homogeneous and better-characterized Foundation sample gives a 55% reduction in the systematic uncertainty attributed to SN Ia sample selection biases. Although use of just a single photometric system at low and high redshift increases the impact of photometric calibration uncertainties in this analysis, previous low-$z$ samples may have correlated calibration uncertainties that were neglected in past studies. The full Foundation sample will observe up to 800 SNe to anchor the LSST and WFIRST Hubble diagrams.Comment: 30 pages, 17 figures, accepted by Ap