A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

Some new examples for nonuniqueness of the evolution problem of harmonic maps

We find some new examples to show nonuniquence for the heat flow of harmonic maps where weak solutions satisfy the same monotonicity property.

Surface foam film waves studied with high-speed linescan camera

Dynamic foam films have been investigated using an improved experimental set-up with a CCD high-speed linescan camera in conjunction with the Scheludko micro-interferometric cell for studying the drainage and rupture of liquid foam films. The improved experimental set-up increased the sensibility of detection of the local thickness heterogeneities and domains during the film evolution. The evolution of the foam films up to the formation of black spots was recorded in the time intervals of 50ms. The wavelengths of the propagating surface waves and their frequencies were determined experimentally. The experimental results show that the current quasi-static hydrodynamic theory does not properly describe the wave dynamics with inter-domain channels. However, the thermodynamic condition for formation of black spots in the foam films was met by the experimental results. (c) 2005 Elsevier B.V. All rights reserved.

Histology of dart tag insertion sites in the epaulette shark

Samples of dermal and epidermal tissues of epaulette sharks Hemiscyllium ocellatum were examined histologically to assess damage caused by tagging. Tissues from around tag sites were removed at time intervals ranging from 100 min to 284 days post-tagging. These samples showed acute and chronic responses to tagging. Acute responses consisted of localized tissue breakdown and haemorrhaging, and occurred within the first few hours after tag insertion. At 10 h post-tagging, an intermediate response was apparent. This phase was characterized by further haemorrhaging and red and white blood cell movement into the wound area. The chronic response observed in the 10-284-day post-tagging samples was characterized by fibrous tissue formation to sequester the tag. This tissue presumably protects the adjacent musculature from further trauma produced by movement of the tag and provides a continuous barrier between the internal and external milieu. Tissue repair appeared to progress consistently in all specimens and no secondary infections at the tag site were seen. Tagging produced only localized tissue disruption and did not appear to be detrimental to the long term health of individual sharks. Our findings show that spaghetti style dart tagging is an acceptable method for marking individuals (40-75+ cm total length) of this species. (C) 1997 The Fisheries Society of the British Isles.

The relationship between leaf water potential and stem diameter in sorghum

Leaf water potential (psi (l)) represents a good indicator of the water status of plants, and continuous monitoring of it can be useful in research and field applications such as scheduling irrigation. Changes in stem diameter (Sd) were used for monitoring psi (l) of pot-grown sorghum [Sorghum bicolor (L.) Moench] plants in a glasshouse. This method requires occasional calibration of S-d values against psi (l). Predicted values of psi (l), based on a single calibration show a good correlation with measured psi (l), values over a period of 13 d before and after the calibration. The correlation can further be improved with shorter time intervals.

Free-radical bulk polymerization of styrene: ESR and near-infrared spectroscopic study of the entire conversion range

The free radical polymerization of styrene in bulk was monitored by ESR and FT near-infrared spectroscopy at 70°C for a series of concentrations of the initiator, dimethyl 2,2′-azobis(isobutyrate). In order to obtain detailed kinetic information over the intire conversion range, and the gel effect range in particular, conversion and free radical concentration data points were accumulated with exceptionally short time intervals. The polystyrene radical concentration ([St•]) went through a sharp maximum at the gel effect, a feature that has hitherto escaped observation due to the rapid concentration changes in the gel effect range relative to the data point time intervals of previous studies. Temperature measurements throughout the polymerization were employed to calculate that a temperature increase was not the cause of the [St•] maximum, which thus appeares to be a genuine feature of the gel effect of this system under isothermal conditions. The propagation rate constant (kp) as a function of monomer conversion exhibited a marked dependence on initiator concentration at high monomer conversion; the sharp decrease in kp with increasing conversion was shifted to higher conversions with increasing initiator concentration.

Determination of the hemispheric character (i.e. southern or northern latitudinal position) of equatorial ionosonde stations as deduced from long-term recordings of the minimum height of the F-region (h ' F)

The virtual (or minimum) height of the F-region (h'F), recorded over a number of solar cycles for I I equatorial and mid-latitude ionosonde stations, was used to deduce the hemispheric (i.e. southern or northern hemisphere) character of equatorial stations. The semi-annual median monthly height (h'F) variations consist of two components: major local summer maximum and winter sub-maximum (about 5 percent of the summer maximum). This hemispheric pattern was most consistently observed for equatorial stations (within 5degrees of the geomagnetic equator) in a period centred on the local midnight (21-03 LT) but was also present, to a lesser extent, at mid-latitude stations and at other time intervals. It is evident that the physical parameter h'F defines the hemispheric character of an equatorial station which has different (sometimes opposite) geographic and geomagnetic latitudes. There is a sharp transition in the latitudinal character of the stations on both sides of the equator leading to hypothesis that the equal maxima in h'F in December and June solstices are observed at a near-equator position labelled as ionosonde deduced equator (IDE). Such a signature was observed for an American equatorial (both geographic and geomagnetic) station Talara (Peru) which is an experimental support of the hypothesis. The IDE can be another useful parameter characterising the equatorial ionosphere. This finding reveals a new application of the standard ionosonde data in defining the geophysical character of equatorial stations, being an important contribution to space climatology. (C) 2002 Elsevier Science Ltd. All rights reserved.

Attachment insecurity, depression, and the transition to parenthood

In a longitudinal study of adult attachment and depression during the transition to parenthood, 76 couples completed questionnaires on three occasions: during the second trimester of pregnancy, and six weeks and six months postbirth. On the first and second occasions, the couples were also interviewed about their experiences of pregnancy and parenthood, respectively. Measures were also completed at similar time intervals by a comparison group of 74 childless couples. Attachment security was assessed in terms of the dimensions of discomfort with closeness and relationship anxiety. Relationship anxiety was less stable for transition wives than for other participants. Relationship anxiety also predicted increases in new mothers' depressive symptoms, after controlling for a broad range of other risk factors. However, the association between relationship anxiety and maternal depression was moderated by husbands' caregiving style. Maternal depression was linked to increases in husbands' and wives' attachment insecurity and marital dissatisfaction. Results are discussed in terms of the impact of depression and negative working models of attachment on couple interaction.

Adaptation is not required to explain the long-term response of axons to molecular gradients

It has been suggested that growth cones navigating through the developing nervous system might display adaptation, so that their response to gradient signals is conserved over wide variations in ligand concentration. Recently however, a new chemotaxis assay that allows the effect of gradient parameters on axonal trajectories to be finely varied has revealed a decline in gradient sensitivity on either side of an optimal concentration. We show that this behavior can be quantitatively reproduced with a computational model of axonal chemotaxis that does not employ explicit adaptation. Two crucial components of this model required to reproduce the observed sensitivity are spatial and temporal averaging. These can be interpreted as corresponding, respectively, to the spatial spread of signaling effects downstream from receptor binding, and to the finite time over which these signaling effects decay. For spatial averaging, the model predicts that an effective range of roughly one-third of the extent of the growth cone is optimal for detecting small gradient signals. For temporal decay, a timescale of about 3 minutes is required for the model to reproduce the experimentally observed sensitivity.

Entangled-state cycles from conditional quantum evolution

A system of cascaded qubits interacting via the one-way exchange of photons is studied. While for general operating conditions the system evolves to a superposition of Bell states (a dark state) in the long-time limit, under a particular resonance condition no steady state is reached within a finite time. We analyze the conditional quantum evolution (quantum trajectories) to characterize the asymptotic behavior under this resonance condition. A distinct bimodality is observed: for perfect qubit coupling, the system either evolves to a maximally entangled Bell state without emitting photons (the dark state) or executes a sustained entangled-state cycle-random switching between a pair of Bell states while emitting a continuous photon stream; for imperfect coupling, two entangled-state cycles coexist, between which a random selection is made from one quantum trajectory to another.

Dark periods and revivals of entanglement in a two-qubit system

In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.

Axiomatisation of an Interval Calculus for Theorem Proving

We provide an axiomatisation of the Timed Interval Calculus, a set-theoretic notation for expressing properties of time intervals. We implement the axiomatisation in the Ergo theorem prover in order to allow the machine-checked proof of laws for reasoning about predicates expressed using interval operators. These laws can be then used in the machine-assisted verification of real-time applications.

Finite-difference time-domain-based studies of MRI pulsed field gradient-induced eddy currents inside the human body

In modern magnetic resonance imaging (MRI), patients are exposed to strong, rapidly switching magnetic gradient fields that, in extreme cases, may be able to elicit nerve stimulation. This paper presents theoretical investigations into the spatial distribution of induced current inside human tissues caused by pulsed z-gradient fields. A variety of gradient waveforms have been studied. The simulations are based on a new, high-definition, finite-difference time-domain method and a realistic inhomogeneous 10-mm resolution human body model with appropriate tissue parameters. it was found that the eddy current densities are affected not only by the pulse sequences but by many parameters such as the position of the body inside the gradient set, the local biological material properties and the geometry of the body. The discussion contains a comparison of these results with previous results found in the literature. This study and the new methods presented herein will help to further investigate the biological effects caused by the switched gradient fields in a MRI scan. (C) 2002 Wiley Periodicals, Inc.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.