Quasi-Local Energy Flux of Spacetime Perturbation

A general expression for quasi-local energy flux for spacetime perturbation is derived from covariant Hamiltonian formulation using functional differentiability and symplectic structure invariance, which is independent of the choice of the canonical variables and the possible boundary terms one initially puts into the Lagrangian in the diffeomorphism invariant theories. The energy flux expression depends on a displacement vector field and the 2-surface under consideration. We apply and test the expression in Vaidya spacetime. At null infinity the expression leads to the Bondi type energy flux obtained by Lindquist, Schwartz and Misner. On dynamical horizons with a particular choice of the displacement vector, it gives the area balance law obtained by Ashtekar and Krishnan.Comment: 8 pages, added appendix, version to appear in Phys. Rev.

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,

Multivariate localization methods for ensemble Kalman filtering

In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (element-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables that exist at the same locations has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help

Rotational coherence of encapsulated ortho and para water in fullerene-C₆₀ revealed by time-domain terahertz spectroscopy

We resolve the real-time coherent rotational motion of isolated water molecules encapsulated in fullerene-C60 cages by time-domain terahertz (THz) spectroscopy. We employ single-cycle THz pulses to excite the low-frequency rotational motion of water and measure the subsequent coherent emission of electromagnetic waves by water molecules. At temperatures below ~ 100 K, C60 lattice vibrational damping is mitigated and the quantum dynamics of confined water are resolved with a markedly long rotational coherence, extended beyond 10 ps. The observed rotational transitions agree well with low-frequency rotational dynamics of single water molecules in the gas phase. However, some additional spectral features with their major contribution at ~2.26 THz are also observed which may indicate interaction between water rotation and the C60 lattice phonons. We also resolve the real-time change of the emission pattern of water after a sudden cooling to 4 K, signifying the conversion of ortho-water to para-water over the course of 10s hours. The observed long coherent rotational dynamics of isolated water molecules confined in C60 makes this system an attractive candidate for future quantum technology

Changing ischaemic lesion patterns in adult moyamoya disease

OBJECTIVES: Ischaemic stroke is a frequent manifestation in patients with adult moyamoya disease (MMD), but the relationship between the lesion pattern and disease severity has rarely been investigated. METHODS: Data were collected on a consecutive series of 65 adult patients with MMD who visited our hospital between 1999 and 2006. Among them, 32 patients with first ever ischaemic stroke were included. The ischaemic lesions were categorised by location and compared as follows: (1) cortical versus subcortical involvement and (2) anterior (fronto-temporal) versus posterior (parieto-occipital) involvement. The lesions were also compared by disease severity, as determined by the extent of intracranial artery involvement (Suzuki's grading method) and by perfusion status visualised on single photon emission computed tomography (SPECT). RESULT: Disease severity was significantly greater in patients with cortical involvement than in those with subcortical involvement (Suzuki's grade 4.17 (0.72) vs 2.70 (0.73); p<0.001). Disease severity was also significantly greater in patients with posterior involvement than in those with anterior involvement (4.50 (0.53) vs 2.83 (0.76); p<0.001). In most of the patients (83.3%) the perfusion defect area shown on SPECT was larger than the ischaemic lesion area shown on MRI. CONCLUSIONS: Patients with advanced stage adult MMD tended to have ischaemic lesions involving the cortex and posterior part of the brain and the stroke mechanism in these patients was largely associated with haemodynamic compromise. Our results suggest that the lesion pattern of ischaemic stroke may change along with the extent of arterial involvement.This study was supported by a grant from the Korea Health 21 R&D Project, Ministry of Health and Welfare, Republic of Korea (A060263)

PENGOLAHAN AIR LIMBAH BUDIDAYA PERIKANAN MELALUI PROSES ANAEROB MENGGUNAKAN BANTUAN MATERIAL BAMBU

The aim of this research was to study the effectivity of bacterium in a simple anaerobic wastewater treatment reactor for degradating the pollutans. The configuration of the reactor used cylindrical plastic material with capacity of 150 L. Meanwhile, the supporting media that used as fixed bed reactor was bamboo with length 23-25 cm, width 3-4 cm, and thickness 0.5 cm. The surface area was 30 m2/m3, 40 m2/m3, and 50 m2/m3 that put into each bioreactor. The biofilm formed in bioreactor and fixed bed medium after cultivating during 30 days. By using the surface area of 50 m2/m3, Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), and ammonia dropped in aquaculture wastewater. The efeciency of BOD5 COD, and ammonia in sampling period test of seven days were 82.28%, 23.08%, and 46.95%, respectively