An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.

Changes in the relative size of the ovary, oviducal glands and eggs are described for Eledone cirrhosa captured from the North Sea off Aberdeen over a 3 year period (N = 488). The analysis is based only on freshly caught animals, excluding those held in aquarium conditions (> 5 days). Ovary enlargement and egg size estimates are used as indices of sexual maturity. Between 0–15% and 18–95% of total body weight is contributed by the ovary. Maximum egg length in the ovary ranges up to 7 mm. On these criteria, sexual maturation typically occurs at body sizes between 400–1000 g although some animals of 1000–1200 g are found showing no evidence of ovary enlargement. The majority of the monthly sample is always immature but maturation can apparently occur at almost any time of the year. Increase in mean ovary index and mean values for egg size are strongly seasonal and indicate a peak incidence of sexual maturity over 2–3 months in the July-September period. Spawning is presumed to follow within 1 month. Estimates of the fecundity of the females, based on the egg sample from the ovary, range from 2·2 × 103 to 55 × 10 3 eggs with a mean of 11 × 10 3 and a mode of 7·5 × 10 3 eggs.

The growth of the octopus Eledone cirrhosa has been studied in a population from the North Sea off Aberdeen. Data are presented for the growth of individuals isolated in aquarium conditions; the growth of size classes in thefieldpopulation; and preliminary information on the growth relationships of gonad, somatic, cardiac and brain components of the body.

At 15 °C Eledone cirrhosa is capable of growing from 10 to 1000 g in 270 days. From octopuses which feed readily in captivity, weight specific growth rates of up to about 3–5 % day-1 for animals of 100 g body weight are recorded, falling to a maximum of about 1–5 % day-1 at body sizes above 500 g. Females stop growing when sexually mature, but in the sample captured they were consistently larger than males, a feature which may account for the 7:1 bias towards the incidence of females. On a wet-weight basis, the mean food incorporation into growth is 37 % of the food ingested, which is 49% of the gross weight of crabs killed. Field data for 1978/79 suggest that animals recruited to the population at the beginning of the year grew steadily until December, overwintered without growing, then grew rapidly for several months in the subsequent year before disappearing from the samples. The estimated average age of those animals and by implication, the life span, is 20 months.

Males of Eledone cirrhosa grow to a size little over 600 g and normally have well-developed, and presumably active, reproductive organs from about 200 g upwards. Total weight of the genital bag is well correlated with total body weight (r= 0·906). Growth of the testis precedes that of the spermatophoric sac, and the size of neither of these reproductive components is predictable from body weight. The sizes of these organs and the estimated number and length of stored spermatophores are given for 100 g intervals of total body weight. No evidence was obtained for a seasonal trend in male maturity.

Female Eledone cirrhosa held in aquarium conditions for periods of time of five daysand over show relatively enlarged ovary sizes. Values for ovary index considerably exceed thoseof freshly caught animals and the incidence of the final stage of maturity, in which eggs pack the oviducts, is greater. A comparison of maturity indices for fresh and aquarium males was inconclusive. The range of factors associated with aquarium conditions is briefly reviewed and it is concluded that studies of cephalopod reproductive maturation must distinguish fresh and aquarium animals.

Introduction

External factors effective in inducing sexual maturation in cephalopods have been suggested several times. The influence of the absence of light has been implicated since the experiments of Wells & Wells (1959) showed that blinded Octopus vulgar is matured precociously. An effect of short day length in stimulating the optic glands of Sepia has been found by Defretin & Richard (1967) and Richard (1967) but this is not clearly the case for Octopus (Buckley, 1977). Octopuses kept in aquarium conditions for lengthy periods are said to have larger relative gonad sizes than those fresh from the sea (Wells & Wells, 1975). One of the factors associated with aquarium conditions is often a degree of starvation, and this circumstance alone is held to be a factor in inducing precocious sexual maturation in Eledone (Mangold & Boucher-Rodoni, 1973).

In the course of recent studies on the growth and reproduction of Eledone cirrhosa from the North Sea (Boyle & Knobloch, 1982,1983,1984) animals which had remained in aquarium conditions for 5 days or over were separated from the analysis.

Asymptotically exact evolution equations for counterpropagating shallow-water edge waves are derived. The structure of the equations depends only on the symmetries of the problem and on the fact that the group velocity of the edge waves is of order one. As a result the equations take the form of parametrically forced Davey–Stewartson equations with mean-field coupling. The calculations extend existing work on parametric excitation of edge waves by normally incident waves to arbitrary beach profiles with asymptotically constant depth, and include coupling to wave-generated mean longshore currents. Dissipation arises generically from radiation damping, but we also consider heuristically the effects of linear boundary-layer damping. Spatially modulated waves do not couple to the parametric forcing due to the non-locality of the evolution equations and are damped. Thus only spatially uniform wavetrains are expected as stable solutions. If linear dissipation is included the parametric coupling selects standing waves, but in the undamped case travelling wave states are possible. Both classes of solutions are examined for modulational instabilities, and stability conditions for the generic evolution equations are presented. However, modulational instability is found to be excluded in the shallow-water formulation through the effects of the mean flow. Explicit numerical results for two experimentally relevant beach profiles, exponentially decaying and piecewise linear, are presented.

Two-dimensional thermosolutal convection is perhaps the simplest example of an idealized fluid dynamical system that displays a rich variety of dynamical behaviour which is amenable to investigation by a combination of analytical and numerical techniques. The transition to chaos found in numerical experiments can be related to behaviour near a multiple bifurcation of codimension three. The resulting third-order normal form equations provide a rational approximation to the governing partial differential equations and thereby confirm that temporal chaos is present in thermosolutal convection. The complex dynamics is associated with a heteroclinic orbit in phase space linking a pair of saddle-foci with eigenvalues satisfying Shil'nikov's criterion. The same bifurcation structure occurs in a truncated fifth-order model and numerical experiments confirm that similar behaviour extends to a significant region of parameter space.

The partial differential equations governing two-dimensional thermosolutal convection in a Boussinesq fluid with free boundary conditions have been solved numerically in a regime where oscillatory solutions can be found. A systematic study of the transition from nonlinear periodic oscillations to temporal chaos has revealed sequences of period-doubling bifurcations. Overstability occurs if the ratio of the solutal to the thermal diffusivity τ < 1 and the solutal Rayleigh number RS is sufficiently large. Solutions have been obtained for two representative values of τ. For τ = 0.316, RS = 104, symmetrical oscillations undergo a bifurcation to asymmetry, followed by a cascade of period-doubling bifurcations leading to aperiodicity, as the thermal Rayleigh number RT is increased. At higher values of RT, the bifurcation sequence is repeated in reverse, restoring simple periodic solutions. As RT is further increased more period-doubling cascades, followed by chaos, can be identified. Within the chaotic regions there are narrow periodic windows, and multiple branches of oscillatory solutions coexist. Eventually the oscillatory branch ends and only steady solutions can be found. The development of chaos has been investigated for τ = 0.1 by varying RT for several different values of RS. When RS is sufficiently small there are periodic solutions whose period becomes infinite at the end of the oscillatory branch. As RS is increased, chaos appears in the neighbourhood of these heteroclinic orbits. At higher values of RS, chaos is found for a broader range in RT. A truncated fifth-order model suggests that the appearance of chaos is associated with heteroclinic bifurcations.

We study two examples of two-dimensional nonlinear double-diffusive convection (thermohaline convection, and convection in an imposed vertical magnetic field) in the limit where the onset of marginal overstability just precedes the exchange of stabilities. In this limit nonlinear solutions can be found analytically. The branch of oscillatory solutions always terminates on the steady solution branch. If the steady solution branch is subcritical this occurs when the period of the oscillation becomes infinite, while if it is supercritical, it occurs via a Hopf bifurcation. A detailed discussion of the stability of the oscillations is given. The results are in broad agreement with the largeramplitude results obtained previously by numerical techniques.

The transport of high-current heavy-ion beams in plasma channels is a promising option for the final transport in a heavy-ion fusion reactor, since it simplifies the construction of the reactor chamber significantly. Our experiments at the Gesellschaft für Schwerionenforschung demonstrate the creation of 1 m long stable plasma channels and the transport of heavy-ion beams. The article outlines the experimental setup used at GSI and reports the results of beam transport measurements using these long channels. The experiments demonstrate good beam transport properties of the channel, indicating that channel transport is a viable alternative to neutralized-ballistic transport.

The final beam transport in the reactor chamber for heavy ion fusion in preformed plasma channels offers many attractive advantages compared to other transport modes. In the past few years, experiments at the Gesellschaft für Schwerionenforschung (GSI) accelerator facility have addressed the creation and investigation of discharge plasmas, designed for the transport of intense ion beams. Stable, self-standing channels of 50 cm length with currents up to 55 kA were initiated in low-pressure ammonia gas by a CO2-laser pulse along the channel axis before the discharge is triggered. The channels were characterized by several plasma diagnostics including interferometry and spectroscopy. We also present first experiments on laser-guided intersecting discharges.

The aim of the presented experiments is to study the transport of a heavy ion beam in a high-current plasma channel. The discharge is initiated in NH3 gas at pressures between 2 and 20 mbar by a line-tuned CO2 laser. A stable discharge over the entire electrode gap (0.5 m) was achieved for currents up to 60 kA. Concerning the ion beam transport, the magnetic field distribution inside the plasma channel has to be known. The ion-optical properties of the plasma channel have been investigated using different species of heavy ions (C, Ni, Au, U) with 11.4 MeV/u during six runs at the Gesellschaft für Schwerionenforschungs-UNILAC linear accelerator. The high magnetic field allowed the accomplishment of one complete betatron oscillation along the discharge channel. The results obtained up to now are very promising and suggest that, by scaling the discharge gap to longer distances, the beam transport over several meters is possible with negligible losses.

Discharge plasma channels have been investigated in recent years at Gesellschaft für Schwerionenforschung–Darmstadt (GSI) and at the Lawrence Berkeley National Laboratory in Berkeley, California, in a number of experiments. A short summary of the experimental work at Berkeley and GSI is given. Different initiation mechanisms for gas discharges of up to 60 kA were studied and compared. In the Berkeley experiments, laser ionization of organic vapors in a buffer gas was used to initiate and direct the discharge while at GSI, laser gas heating and ion-beam-induced gas ionization were tested as initiation mechanisms. These three initiation techniques are compared and the stability of the resulting discharge channels is discussed. A discharge current of 50 kA, a channel diameter well below 1 cm, a pointing stability better than 200 μm, and MHD stability of more than 10 μs have been demonstrated simultaneously in the recent experiments. These parameters are sufficient or close to the requirements of a reactor application depending on the details of the target design. The experimental results show that transport channels work with sufficient stability, reproducibility, and ion optical properties for a wide pressure range of discharge gases and pressures.

We have studied optical properties of GaN grown on sapphire by metalorganic chemical vapor deposition in the near band-edge energy range by cathodoluminescence. A large shift of the band-edge luminescence to lower energies is induced by increasing the beam energy. The free exciton position shifts about 20 meV when the beam energy is increased from 5 keV to 25 keV at room-temperature. The effect is explained by internal absorption caused by an exponential absorption tail at the band-edge. An Urbach parameter of about 30 to 40 meV for the exponential band-tail in our samples is estimated by comparing experimental with simulated spectra.