Bondi mass with a cosmological constant

The mass loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant $\Lambda\in\R$ was recently worked out, using the Newman-Penrose-Unti approach. In that same article, an expression for the Bondi mass of the isolated system, $M_\Lambda$, for the $\Lambda>0$ case was proposed. The stipulated mass $M_\Lambda$ would ensure that in the absence of any incoming gravitational radiation from elsewhere, the emitted gravitational waves must carry away a positive-definite energy. That suggested quantity however, introduced a $\Lambda$-correction term to the Bondi mass $M_B$ (where $M_B$ is the usual Bondi mass for asymptotically flat spacetimes) which would involve not just information on the state of the system at that moment, but ostensibly also its past history. In this paper, we derive the identical mass-loss equation using an integral formula on a hypersurface formulated by Frauendiener based on the Nester-Witten identity, and argue that one may adopt a generalisation of the Bondi mass with $\Lambda\in\R$ \emph{without any correction}, viz. $M_\Lambda=M_B$ for any $\Lambda\in\R$. Furthermore with $M_\Lambda=M_B$, we show that for \emph{purely quadrupole gravitational waves} given off by the isolated system (i.e. when the "Bondi news" $\sigma^o$ comprises only the $l=2$ components of the "spherical harmonics with spin-weight 2"), the energy carried away is \emph{manifestly positive-definite} for the $\Lambda>0$ case. For a general $\sigma^o$ having higher multipole moments, this perspicuous property in the $\Lambda>0$ case still holds if those $l>2$ contributions are weak --- more precisely, if they satisfy any of the inequalities given in this paper.Comment: 29 pages, accepted for publication by Physical Review

Power saw

A power saw is disclosed for space or robotic operations with jaw members for clamping to a work piece by an operation of a lever arm. The saw assembly is slidably mounted on the jaw assembly and fed into the work piece by a hand operated feed screw. The saw assembly includes a motor and gear belt. A current sensing circuit provides a current signal which actuates colored lights to visually depict the load on the saw blade during the cutting operations

Helicalised fractals

We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line and circle, showing that it takes the form of the self-similar dimension for a self-similar fractal, with lower bound of 1. Upper bounds to the Hausdorff dimension as functions of $\omega$ have been determined for the linear helical fractal, curved helical fractal and circular fractal, based on the no-self-intersection constraint. For large number of windings $\omega\rightarrow\infty$, the upper bounds all have the limit of 2. This would suggest that carrying out a topological analysis on the structure of chromosomes by modelling it as a two-dimensional surface may be beneficial towards further understanding on the dynamics of DNA packaging.Comment: 25 pages, 10 figures. v3: Detailed derivation of the Hausdorff dimension included. Accepted by Chaos, Solitons & Fractal

Field experience with various slicing methods

Wafer slicing using internal diameter (ID) saw, multiblade slurry (MBS) saw and multiwire slurry (MWS) saw techniques were evaluated. Wafer parameters such as bow, taper, and roughness which may not be important factors for solar cell fabrication, were considerably better for ID saw than those of the MBS and MWS saw. Analysis of add-on slicing cost indicated that machine productivity seems to be a major limiting factor for ID saw, while expendible material costs are a major factor for both MBS and MWS saw. Slicing experience indicated that the most important factors controling final wafer cost are: (1) silicon cost (wafer thickness + kerf loss); (2) add-on slicing cost, and (3) mechanical yield. There is a very strong interaction between these parameters, suggesting a necessity of optimization of these parameters

See-Saw Modification of Gravity

We discuss a model in which the fundamental scale of gravity is restricted to 10^{-3} eV. An observable modification of gravity occurs simultaneously at the Hubble distance and at around 0.1 mm. These predictions can be tested both by the table-top experiments and by cosmological measurements. The model is formulated as a brane-world theory embedded in a space with two or more infinite-volume extra dimensions. Gravity on the brane reproduces the four-dimensional laws at observable distances but turns to the high-dimensional behavior at larger scales. To determine the crossover distance we smooth out the singularities in the Green's functions by taking into account softening of the graviton propagator due to the high-dimensional operators that are suppressed by the fundamental scale. We find that irrespective of the precise nature of microscopic gravity the ultraviolet and infrared scales of gravity-modification are rigidly correlated. This fixes the fundamental scale of gravity at 10^{-3} eV. The result persists for nonzero thickness branes.Comment: 24 LaTex pages; v2: comments added, typos correcte