Haemoglobin and size dependent constraints on swimbladder inflation in fish larvae

In developmental studies of fish species (especially physostomians) it could be demonstrated, that the lack of haemoglobin during larval and juvenile stages is a relatively common phenomenon. Generally it is linked with body translucency. In representatives of the families Galaxiidae, Osmeridae and Clupeidae, partly reared, partly observed immediately after being caught in the wild, it turned out, that this condition coincides with a considerable delay in swimbladder inflation. To determine the moment of its first inflation, larvae placed in a hermetic chamber were observed under a dissecting microscope. While lowering the pressure, the expanding swimbladder showed whether or not its content is really gaseous. The reason postulated to be responsible for the delayed inflation is that larvae lacking haemoglobin do not have the possibility of oxygen transport to their buoyancy organ by means of the blood. Apart of this, capillarity force calculations and body force estimations show that with decreasing size the constraints linked with surface tension increase overproportionally. While in larger sized larvae like trout we could demonstrate inflation by swallowing air, in species with small larvae this was not the case. Below a certain size, even in physostomians, the ductus pneumaticus is no alternative to the blood pathway for swimbladder inflation

Loop space, (2,0) theory, and solitonic strings

We present an interacting action that lives in loop space, and we argue that this is a generalization of the theory for a free tensor multiplet. From this action we derive the Bogomolnyi equation corresponding to solitonic strings. Using the Hopf map, we find a correspondence between BPS strings and BPS monopoles in four-dimensional super Yang-Mills theory. This enable us to find explicit BPS saturated solitonic string solutions.Comment: 29 pages, v3: section 5 is rewritten and string solutions are found, v4: a new section on general covariance in loop spac

On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

The visual sociogram in qualitative and mixed-methods research

The paper investigates the place of visual tools in mixed-methods research on social networks, arguing that they can not only improve the communicability of results, but also support research at the data gathering and analysis stages. Three examples from the authors’ own research experience illustrate how sociograms can be integrated in multiple ways with other analytical tools, both quantitative and qualitative, positioning visualization at the intersection of varied methods and channelling substantive ideas as well as network insight in a coherent way. Visualization also facilitates the participation of a broad range of stakeholders, including among others, study participants and non-specialist researchers. It can support the capacity of qualitative and mixed-methods research to reach out to areas of the social that are difficult to circumscribe, such as hidden populations and informal organisations. On this basis, visualization appears as a unique opportunity for mixing methods in the study of social networks, emphasizing both structure and process at the same time

Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivariant de Rham cohomology in terms of derived functors developed earlier for the special case where the Lie groupoid is an ordinary Lie group, viewed as a Lie groupoid with a single object; in that theory over a Lie group, the ordinary Bott-Dupont-Shulman-Stasheff complex arises as an a posteriori object. We prove that, given a locally trivial Lie groupoid G and a smooth G-manifold f over the space B of objects of G, the resulting G-equivariant de Rham theory of f boils down to the ordinary equivariant de Rham theory of a vertex manifold relative to the corresponding vertex group, for any vertex in the space B of objects of G; this implies that the equivariant de Rham cohomology introduced here coincides with the stack de Rham cohomology of the associated transformation groupoid whence this stack de Rham cohomology can be characterized as a relative derived functor. We introduce a notion of cone on a Lie-Rinehart algebra and in particular that of cone on a Lie algebroid. This cone is an indispensable tool for the description of the requisite monads.Comment: 47 page

Static solitons with non-zero Hopf number

We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made, a reference has been corrected and a figure replace

Relaxation and reconstruction on (111) surfaces of Au, Pt, and Cu

We have theoretically studied the stability and reconstruction of (111) surfaces of Au, Pt, and Cu. We have calculated the surface energy, surface stress, interatomic force constants, and other relevant quantities by ab initio electronic structure calculations using the density functional theory (DFT), in a slab geometry with periodic boundary conditions. We have estimated the stability towards a quasi-one-dimensional reconstruction by using the calculated quantities as parameters in a one-dimensional Frenkel-Kontorova model. On all surfaces we have found an intrinsic tensile stress. This stress is large enough on Au and Pt surfaces to lead to a reconstruction in which a denser surface layer is formed, in agreement with experiment. The experimentally observed differences between the dense reconstruction pattern on Au(111) and a sparse structure of stripes on Pt(111) are attributed to the details of the interaction potential between the first layer of atoms and the substrate.Comment: 8 pages, 3 figures, submitted to Physical Review

A Texture Bestiary

Textures are topologically nontrivial field configurations which can exist in a field theory in which a global symmetry group $G$ is broken to a subgroup $H$, if the third homotopy group \p3 of $G/H$ is nontrivial. We compute this group for a variety of choices of $G$ and $H$, revealing what symmetry breaking patterns can lead to texture. We also comment on the construction of texture configurations in the different models.Comment: 34 pages, plain Tex. (Minor corrections to an old paper.