Space use by passerine birds : a study of territory economics in robins Erithacus rubecula and dippers Cinclus cinclus

1. Cost constraints in models of territory size are based on time/activity/laboratory estimates that predict birds using larger territories will incur higher energy costs. The predicted form of the cost constraint may be linear, accelerating or decelerating depending on assumptions inherent in the models. The aim of this study was to assess the reality and form of the cost constraint by making direct measurements of the energy costs of territory use in birds that occupy territories of different size and shape; polygonal territories represented by the robin Erithacus rubecula, and linear by the dipper Cinclus cinclus. Free-living energy expenditure was measured using the doubly-labelled water technique, whilst simultaneously recording patterns of territory use by radio-tracking. 2. Territorial robins concentrated their activity in one or more foraging patches located in bushes. Range polygons containing all the foraging patches used by an individual provided estimates of territory area, and were generally of high eccentricity. A small proportion of robins was classified as non-territorial based on range polygon areas. Furthermore, while territorial robins showed high fidelity to ranges over the short term (days), non-territorial individuals were nomadic. Over the longer term (months), however, some territorial robins showed range drift. Dippers similarly used preferred core regions within ranges, although there was no selection for particular habitat features. 3. Because robins occupied territory polygons which varied from polygonal to highly linear, work was focused on this species to allow intra-specific comparison. Robins tended to commute between foraging patches by flying. It was appropriate, therefore, to describe territories in terms of a number of patches linked by a network of flight paths. This generated two further measures of territory size; the number of patches used and the total flight distance between patches. 4. The robins exploited a renewing food supply. Predictions were tested concerning the temporal scheduling of visits to foraging patches within territories. Patches tended to be separated by flight paths of similar lengths, and were visited in a regular sequence. Although the number of foraging patches used varied, all territories had similar total core areas. Robins using many small foraging patches commuted between patches more often and covered a larger total flight distance during each foraging circuit of the territory. The configurations of foraging patches were used in a highly linear manner. This was true even if the territory containing them was of low eccentricity. 5. Changes in structure and pattern of use varied predictably with territory size, and could be described mathematically. Based on this and published time/activity budgets, a suite of models was developed to predict how energy costs would vary with number of patches used and total flight distance between patches. Models were tested by directly measuring the energy expenditure of robins using different territories. The number of patches used and total flight distance between patches were both significantly correlated with energy expenditure, while territory area was not. One of the models showed a significant fit to the observed data, and suggested that the form of the energy cost constraint on territory size was linear. The effect of territory shape on energy costs was minimal. The implications of these results for models of territory size are discussed. 6. The slope and elevation of the energy cost constraint varied with the morphology of territory occupants. Based on this, an association of morphology with territory size was predicted; robins of lower mass and wing-loading using larger territories. The observed data supported these predictions, and suggested a possible genetic predisposition to particular patterns of territory occupancy in the robin

Stellar Winds on the Main-Sequence I: Wind Model

Aims: We develop a method for estimating the properties of stellar winds for low-mass main-sequence stars between masses of 0.4 and 1.1 solar masses at a range of distances from the star. Methods: We use 1D thermal pressure driven hydrodynamic wind models run using the Versatile Advection Code. Using in situ measurements of the solar wind, we produce models for the slow and fast components of the solar wind. We consider two radically different methods for scaling the base temperature of the wind to other stars: in Model A, we assume that wind temperatures are fundamentally linked to coronal temperatures, and in Model B, we assume that the sound speed at the base of the wind is a fixed fraction of the escape velocity. In Paper II of this series, we use observationally constrained rotational evolution models to derive wind mass loss rates. Results: Our model for the solar wind provides an excellent description of the real solar wind far from the solar surface, but is unrealistic within the solar corona. We run a grid of 1200 wind models to derive relations for the wind properties as a function of stellar mass, radius, and wind temperature. Using these results, we explore how wind properties depend on stellar mass and rotation. Conclusions: Based on our two assumptions about the scaling of the wind temperature, we argue that there is still significant uncertainty in how these properties should be determined. Resolution of this uncertainty will probably require both the application of solar wind physics to other stars and detailed observational constraints on the properties of stellar winds. In the final section of this paper, we give step by step instructions for how to apply our results to calculate the stellar wind conditions far from the stellar surface.Comment: 24 pages, 13 figures, 2 tables, Accepted for publication in A&

Effect of stellar wind induced magnetic fields on planetary obstacles of non-magnetized hot Jupiters

We investigate the interaction between the magnetized stellar wind plasma and the partially ionized hydrodynamic hydrogen outflow from the escaping upper atmosphere of non- or weakly magnetized hot Jupiters. We use the well-studied hot Jupiter HD 209458b as an example for similar exoplanets, assuming a negligible intrinsic magnetic moment. For this planet, the stellar wind plasma interaction forms an obstacle in the planet's upper atmosphere, in which the position of the magnetopause is determined by the condition of pressure balance between the stellar wind and the expanded atmosphere, heated by the stellar extreme ultraviolet (EUV) radiation. We show that the neutral atmospheric atoms penetrate into the region dominated by the stellar wind, where they are ionized by photo-ionization and charge exchange, and then mixed with the stellar wind flow. Using a 3D magnetohydrodynamic (MHD) model, we show that an induced magnetic field forms in front of the planetary obstacle, which appears to be much stronger compared to those produced by the solar wind interaction with Venus and Mars. Depending on the stellar wind parameters, because of the induced magnetic field, the planetary obstacle can move up to ~0.5-1 planetary radii closer to the planet. Finally, we discuss how estimations of the intrinsic magnetic moment of hot Jupiters can be inferred by coupling hydrodynamic upper planetary atmosphere and MHD stellar wind interaction models together with UV observations. In particular, we find that HD 209458b should likely have an intrinsic magnetic moment of 10-20% that of Jupiter.Comment: 8 pages, 6 figures, 2 tables, accepted to MNRA

A Critique of Current Magnetic-Accretion Models for Classical T-Tauri Stars

Current magnetic-accretion models for classical T-Tauri stars rely on a strong, dipolar magnetic field of stellar origin to funnel the disk material onto the star, and assume a steady-state. In this paper, I critically examine the physical basis of these models in light of the observational evidence and our knowledge of magnetic fields in low-mass stars, and find it lacking. I also argue that magnetic accretion onto these stars is inherently a time-dependent problem, and that a steady-state is not warranted. Finally, directions for future work towards fully-consistent models are pointed out.Comment: 2 figure

Hitting Time of Quantum Walks with Perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.Comment: 9 page

Emergence of fractal behavior in condensation-driven aggregation

We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision. We solved the model exactly by using scaling theory for the case whereby a particle, say of size $x$, grows by an amount $\alpha x$ over the time it takes to collide with another particle of any size. It is shown that the particle size spectra of such system exhibit transition to dynamic scaling $c(x,t)\sim t^{-\beta}\phi(x/t^z)$ accompanied by the emergence of fractal of dimension $d_f={{1}\over{1+2\alpha}}$. One of the remarkable feature of this model is that it is governed by a non-trivial conservation law, namely, the $d_f^{th}$ moment of $c(x,t)$ is time invariant regardless of the choice of the initial conditions. The reason why it remains conserved is explained by using a simple dimensional analysis. We show that the scaling exponents $\beta$ and $z$ are locked with the fractal dimension $d_f$ via a generalized scaling relation $\beta=(1+d_f)z$.Comment: 8 pages, 6 figures, to appear in Phys. Rev.