Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions

We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying ``energy-momentum'' vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the resulting Dirichlet and Neumann vectors for topologically spherical 2-surfaces in Minkowski spacetime, spherically symmetric spacetimes, and stationary axisymmetric spacetimes. Moreover, we show the relation between these vectors and the ADM energy-momentum vector for a 2-surface taken in a limit to be spatial infinity in asymptotically flat spacetimes. We also discuss the geometrical properties of the Dirichlet and Neumann vectors and obtain several striking results relating these vectors to the mean curvature and normal curvature connection of the 2-surface. Most significantly, the part of the Dirichlet vector normal to the 2-surface depends only the spacetime metric at this surface and thereby defines a geometrical normal vector field on the 2-surface. Properties and examples of this normal vector are discussed.Comment: 46 pages; minor errata corrected in Eqs. (3.15), (3.24), (4.37) and in discussion of examples in sections IV B,

Rigid motion revisited: rigid quasilocal frames

We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a "system" in general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (constant size) and shear-free (constant shape). This definition of a system is anticipated to yield simple, exact geometrical insights into the problem of motion in general relativity. It begins by answering the questions what is in motion (a rigid two-dimensional system boundary), and what motions of this rigid boundary are possible. Nearly a century ago Herglotz and Noether showed that a three-parameter family of timelike worldlines in Minkowski space satisfying Born's 1909 rigidity conditions has only three degrees of freedom instead of the six we are familiar with from Newtonian mechanics. We argue that in fact we can implement Born's notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent papers) - with precisely the expected three translational and three rotational degrees of freedom - provided the system is defined quasilocally as the two-dimensional set of points comprising the boundary of a finite spatial volume, rather than the three-dimensional set of points within the volume.Comment: 10 pages (two column), 24 pages (preprint), 1 figur

Grasses continue to trump trees at soil carbon sequestration following herbivore exclusion in a semiarid African savanna

Although studies have shown that mammalian herbivores often limit aboveground carbon storage in savannas, their effects on belowground soil carbon storage remain unclear. Using three sets of long‐term, large herbivore exclosures with paired controls, we asked how almost two decades of herbivore removal from a semiarid savanna in Laikipia, Kenya affected aboveground (woody and grass) and belowground soil carbon sequestration, and determined the major source (C3 vs. C4) of belowground carbon sequestered in soils with and without herbivores present. Large herbivore exclusion, which included a diverse community of grazers, browsers, and mixed‐feeding ungulates, resulted in significant increases in grass cover (~22%), woody basal area (~8 m2/ha), and woody canopy cover (31%), translating to a ~8.5 t/ha increase in aboveground carbon over two decades. Herbivore exclusion also led to a 54% increase (20.5 t/ha) in total soil carbon to 30‐cm depth, with ~71% of this derived from C4 grasses (vs. ~76% with herbivores present) despite substantial increases in woody cover. We attribute this continued high contribution of C4 grasses to soil C sequestration to the reduced offtake of grass biomass with herbivore exclusion together with the facilitative influence of open sparse woody canopies (e.g., Acacia spp.) on grass cover and productivity in this semiarid system

Selected Topics in High Energy Semi-Exclusive Electro-Nuclear Reactions

We review the present status of the theory of high energy reactions with semi-exclusive nucleon electro-production from nuclear targets. We demonstrate how the increase of transferred energies in these reactions opens a complete new window in studying the microscopic nuclear structure at small distances. The simplifications in theoretical descriptions associated with the increase of the energies are discussed. The theoretical framework for calculation of high energy nuclear reactions based on the effective Feynman diagram rules is described in details. The result of this approach is the generalized eikonal approximation (GEA), which is reduced to Glauber approximation when nucleon recoil is neglected. The method of GEA is demonstrated in the calculation of high energy electro-disintegration of the deuteron and A=3 targets. Subsequently we generalize the obtained formulae for A>3 nuclei. The relation of GEA to the Glauber theory is analyzed. Then based on the GEA framework we discuss some of the phenomena which can be studied in exclusive reactions, these are: nuclear transparency and short-range correlations in nuclei. We illustrate how light-cone dynamics of high-energy scattering emerge naturally in high energy electro-nuclear reactions.Comment: LaTex file with 51 pages and 23 eps figure

Using appreciative inquiry to implement person-centred dementia care in hospital wards

The quality of care of persons with dementia in hospitals is not optimal and can be challenging. Moreover, staff may find difficulty in translating what they have learned during training into practice. This paper report the development and evaluation of a set of workshops using an Appreciative Inquiry (AI) approach to implement person-centred dementia care in two hospital wards. Staff worked collaboratively to develop a ward vision and to implement a number of action plans. Using AI approach, staff attitudes towards persons with dementia improved, inter-professional collaboration was enhanced and small changes in staff practices were noted. Dementia care in hospitals can be enhanced by empowering staff to take small but concrete actions after they engage in AI workshops, during which they are listened to and appreciated for what they can contribute

Angular momentum and an invariant quasilocal energy in general relativity

Owing to its transformation property under local boosts, the Brown-York quasilocal energy surface density is the analogue of E in the special relativity formula: E^2-p^2=m^2. In this paper I will motivate the general relativistic version of this formula, and thereby arrive at a geometrically natural definition of an `invariant quasilocal energy', or IQE. In analogy with the invariant mass m, the IQE is invariant under local boosts of the set of observers on a given two-surface S in spacetime. A reference energy subtraction procedure is required, but in contrast to the Brown-York procedure, S is isometrically embedded into a four-dimensional reference spacetime. This virtually eliminates the embeddability problem inherent in the use of a three-dimensional reference space, but introduces a new one: such embeddings are not unique, leading to an ambiguity in the reference IQE. However, in this codimension-two setting there are two curvatures associated with S: the curvatures of its tangent and normal bundles. Taking advantage of this fact, I will suggest a possible way to resolve the embedding ambiguity, which at the same time will be seen to incorporate angular momentum into the energy at the quasilocal level. I will analyze the IQE in the following cases: both the spatial and future null infinity limits of a large sphere in asymptotically flat spacetimes; a small sphere shrinking toward a point along either spatial or null directions; and finally, in asymptotically anti-de Sitter spacetimes. The last case reveals a striking similarity between the reference IQE and a certain counterterm energy recently proposed in the context of the conjectured AdS/CFT correspondence.Comment: 54 pages LaTeX, no figures, includes brief summary of results, submitted to Physical Review

Imaging Molecular Structure through Femtosecond Photoelectron Diffraction on Aligned and Oriented Gas-Phase Molecules

This paper gives an account of our progress towards performing femtosecond time-resolved photoelectron diffraction on gas-phase molecules in a pump-probe setup combining optical lasers and an X-ray Free-Electron Laser. We present results of two experiments aimed at measuring photoelectron angular distributions of laser-aligned 1-ethynyl-4-fluorobenzene (C8H5F) and dissociating, laseraligned 1,4-dibromobenzene (C6H4Br2) molecules and discuss them in the larger context of photoelectron diffraction on gas-phase molecules. We also show how the strong nanosecond laser pulse used for adiabatically laser-aligning the molecules influences the measured electron and ion spectra and angular distributions, and discuss how this may affect the outcome of future time-resolved photoelectron diffraction experiments.Comment: 24 pages, 10 figures, Faraday Discussions 17

Communication: X-ray coherent diffractive imaging by immersion in nanodroplets

Citation: Tanyag, R. M. P., Bernando, C., Jones, C. F., Bacellar, C., Ferguson, K. R., Anielski, D., . . . Vilesov, A. F. (2015). Communication: X-ray coherent diffractive imaging by immersion in nanodroplets. Structural Dynamics, 2(5), 9. doi:10.1063/1.4933297Lensless x-ray microscopy requires the recovery of the phase of the radiation scattered from a specimen. Here, we demonstrate a de novo phase retrieval technique by encapsulating an object in a superfluid helium nanodroplet, which provides both a physical support and an approximate scattering phase for the iterative image reconstruction. The technique is robust, fast-converging, and yields the complex density of the immersed object. Images of xenon clusters embedded in superfluid helium droplets reveal transient configurations of quantum vortices in this fragile system. (C) 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.Additional Authors: Neumark, D. M.;Rolles, D.;Rudek, B.;Rudenko, A.;Siefermann, K. R.;Ullrich, J.;Weise, F.;Bostedt, C.;Gessner, O.;Vilesov, A. F

Feynman Graphs and Generalized Eikonal Approach to High Energy Knock-Out Processes

The cross section of hard semi-exclusive $A(e,e'N)(A-1)$ reactions for fixed missing energy and momentum is calculated within the eikonal approximation. Relativistic dynamics and kinematics of high energy processes are unambiguously accounted for by using the analysis of appropriate Feynman diagrams. A significant dependence of the final state interactions on the missing energy is found, which is important for interpretation of forthcoming color transparency experiments. A new, more stringent kinematic restriction on the region where the contribution of short-range nucleon correlations is enhanced in semi-exclusive knock-out processes is derived. It is also demonstrated that the use of light-cone variables leads to a considerable simplification of the description of high-energy knock-out reactions.Comment: 24 pages, LaTex, two Latex and two ps figures, uses FEYNMAN.tex and psfig.sty. Revisied version to appear in Phys. Rev.

QED on Curved Background and on Manifolds with Boundaries: Unitarity versus Covariance

Some recent results show that the covariant path integral and the integral over physical degrees of freedom give contradicting results on curved background and on manifolds with boundaries. This looks like a conflict between unitarity and covariance. We argue that this effect is due to the use of non-covariant measure on the space of physical degrees of freedom. Starting with the reduced phase space path integral and using covariant measure throughout computations we recover standard path integral in the Lorentz gauge and the Moss and Poletti BRST-invariant boundary conditions. We also demonstrate by direct calculations that in the approach based on Gaussian path integral on the space of physical degrees of freedom some basic symmetries are broken.Comment: 29 pages, LaTEX, no figure