The structure of spider's web fast escaping sets

Building on recent work by Rippon and Stallard, we explore the intricate structure of the spider's web fast escaping sets associated with certain transcendental entire functions. Our results are expressed in terms of the components of the complement of the set (the 'holes' in the web). We describe the topology of such components and give a characterisation of their possible orbits under iteration. We show that there are uncountably many components having each of a number of orbit types, and we prove that components with bounded orbits are quasiconformally homeomorphic to components of the filled Julia set of a polynomial. We also show that there are singleton periodic components and that these are dense in the Julia set.Comment: 18 page

Quantitative estimates of fish abundance from boat electrofishing

Multiple removals by boat electro-fishing were used to estimate fish populations in non-wadeable habitats in New Zealand lakes and rivers. Mean capture probability was 0.47±h0.10 (± 95% CI) from 35 population estimates made with 2-7 successive removals. The relationship between the population estimate from the Zippin method (Y)and the number of fish caught in the first removal (X) was significant (adjusted r2=0.84, P<0.001; Figure 2). The least-squares regression was Y = 1.55X 1.23. Mean density ± 95% confidence interval for 13 fishing occasions was 30±27 fish 100 m- 2. Mean biomass of fish for sites was 78±39 g m-2 (range 29 to 245 g m-2). Koi carp comprised the largest proportion of the fish biomass wherever they were present. The high biomasses of koi carp estimated in these results (mean 56±33 g m-2) suggest that they can reach problematic abundances in New Zealand. Bioniass of spawning koi carp can exceed 400 g m-2

Pure xenon hexafluoride prepared for thermal properties studies

Preparation of a xenon hexafluoride and sodium fluoride salt yields a sample of the highest possible purity for use in thermal measurements. The desired hexafluoride can easily be freed from the common contaminants, xenon tetra-fluoride, xenon difluoride, and xenon oxide tetrafluoride, because none of these compounds reacts with sodium fluoride

Age composition, growth, and reproduction of koi carp (Cyprinus carpio L.) in the lower Waikato, New Zealand

A total of 566 koi carp (Cyprinus carpio) from the lower Waikato region were aged from scales and opercular bones, and growth was modelled with the von Bertalanffy growth function. There was no difference in growth rate between male and female carp. Growth of koi carp between zero and 3 years of age was lower than that of common carp in Europe and Australia. However, after 5 years of age the growth of koi carp was higher than that of common carp in Europe, but still below that of carp in Australia. Males rarely lived in excess of 8 years, whereas females lived to 12 years. Mean total fecundity calculated from 44 running-ripe females was 299 000 oocytes (±195 600 SD) (range 29 800–771 000). Relative fecundity ranged from 19 300 to 216 000 oocytes kg–1 total body weight, with a mean of 97 200 (±35 000 SD) oocytes kg–1. Feral koi carp in the Waikato are capable of multiple spawnings within their lifetimes. Within a spawning season, Waikato populations of feral koi carp contained females that spawned once, and females that had the potential to have spawned repeatedly. Female gonadosomatic index (GSI) varied with season and was negatively related to water temperature

Connectedness properties of the set where the iterates of an entire function are unbounded

We investigate the connectedness properties of the set I+(f) of points where the iterates of an entire function f are unbounded. In particular, we show that I+(f) is connected whenever iterates of the minimum modulus of f tend to ∞. For a general transcendental entire function f, we show that I+(f)∪ \{\infty\} is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded

Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit

We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite region with fixed boundary conditions. The suppression of unphysical quasiparticle reflections from the boundary of the nonuniform region is also discussed. Using this algorithm we study the dynamics of localized excitations in infinite systems, which we illustrate in the case of the spin-1 anti-ferromagnetic Heisenberg model and the $\phi^4$ model.Comment: 8 pages, 5 figures, tensor network diagrams. Code available at http://amilsted.github.io/evoMPS

The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently

We study families H_n of 1D quantum spin systems, where n is the number of spins, which have a spectral gap \Delta E between the ground-state and first-excited state energy that scales, asymptotically, as a constant in n. We show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins, where m is an O(1) constant, is locally the same as the ground state |\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to the ground state of H_n can be stored efficiently for all n. We formulate a conjecture that, if true, would imply our result applies to all noncritical 1D spin systems. We also include an appendix on quasi-adiabatic evolutions.Comment: 9 pages, 1 eps figure, minor change

Achievable Qubit Rates for Quantum Information Wires

Suppose Alice and Bob have access to two separated regions, respectively, of a system of electrons moving in the presence of a regular one-dimensional lattice of binding atoms. We consider the problem of communicating as much quantum information, as measured by the qubit rate, through this quantum information wire as possible. We describe a protocol whereby Alice and Bob can achieve a qubit rate for these systems which is proportional to N^(-1/3) qubits per unit time, where N is the number of lattice sites. Our protocol also functions equally in the presence of interactions modelled via the t-J and Hubbard models