Modified gravity without dark matter

On an empirical level, the most successful alternative to dark matter in bound gravitational systems is the modified Newtonian dynamics, or MOND, proposed by Milgrom. Here I discuss the attempts to formulate MOND as a modification of General Relativity. I begin with a summary of the phenomenological successes of MOND and then discuss the various covariant theories that have been proposed as a basis for the idea. I show why these proposals have led inevitably to a multi-field theory. I describe in some detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and discuss its successes and shortcomings. This lecture is primarily pedagogical and directed to those with some, but not a deep, background in General RelativityComment: 28 pages, 10 figures, lecture given at Third Aegean Summer School, The Invisible Universe: Dark Matter and Dark Energy, minor errors corrected, references update

QUANTIFYING LIFT AND DRAG FORCES IN FLATWATER KAYAKING

The purpose of this study was to develop a method of determining lift and drag forces produced by the 'wing' blade In flatwater kayaking using data digitised from cine film or videotape. The method involves six operations. 1. Recording by two cameras on film or videotape known positions of points on a three dimensional calibration frame, two reference points on the kayak, and three reference points on the shaft of the paddle. 2. Obtaining the three dimensional positions of the digitised markers using the Direct Linear Transformation (DLT) method, 3. Determining the path of the blade and its orientation with respect to the external reference frame. 4. Calculating the 'sweepback' and 'pitch' angles of the Made using the direction of the blade centre path as the reference. 5. Applying known lift and drag coefficients for each calculated sweepback and pitch angle combination to determine the magnitude of the lift and drag force vectors at each sampled instant. 6. Determining the components of the lift and drag force vectors in the desired direction of travel and using these to calculate the efficiency of the lift and drag vectors. Reliability of the method has been estimated for the operations up to operation 4 using data obtained from elite New Zealand flatwater kayak paddlers under simulated competition conditions. Research initiated by the first author at the International Center for Aquatic Research to determine the lift and drag coefficients for any given sweepback and pitch angle combination is continuing. This paper describes the operations outlined above and presents some reliability data for these operations

Testing quantised inertia on galactic scales

Galaxies and galaxy clusters have rotational velocities apparently too fast to allow them to be gravitationally bound by their visible matter. This has been attributed to the presence of invisible (dark) matter, but so far this has not been directly detected. Here, it is shown that a new model that modifies inertial mass by assuming it is caused by Unruh radiation, which is subject to a Hubble-scale (Theta) Casimir effect predicts the rotational velocity (v) to be: v^4=2GMc^2/Theta (the Tully-Fisher relation) where G is the gravitational constant, M is the baryonic mass and c is the speed of light. The model predicts the outer rotational velocity of dwarf and disk galaxies, and galaxy clusters, within error bars, without dark matter or adjustable parameters, and makes a prediction that local accelerations should remain above 2c^2/Theta at a galaxy's edge.Comment: 7 pages, 1 figure. Accepted for publication in Astrophysics and Space Science on 27/7/201

Pure mathematics in Australia

I.D. Macdonald argued in this journal in 1968 that there was an inadequate number of mathematicians teaching in Australian universities who were qualified by international standards to conduct honours courses and supervise research students..

A solution for galactic disks with Yukawian gravitational potential

We present a new solution for the rotation curves of galactic disks with gravitational potential of the Yukawa type. We follow the technique employed by Toomre in 1963 in the study of galactic disks in the Newtonian theory. This new solution allows an easy comparison between the Newtonian solution and the Yukawian one. Therefore, constraints on the parameters of theories of gravitation can be imposed, which in the weak field limit reduce to Yukawian potentials. We then apply our formulae to the study of rotation curves for a zero-thickness exponential disk and compare it with the Newtonian case studied by Freeman in 1970. As an application of the mathematical tool developed here, we show that in any theory of gravity with a massive graviton (this means a gravitational potential of the Yukawa type), a strong limit can be imposed on the mass (m_g) of this particle. For example, in order to obtain a galactic disk with a scale length of b ~ 10 kpc, we should have a massive graviton of m_g << 10^{-59} g. This result is much more restrictive than those inferred from solar system observations.Comment: 7 pages; 1 eps figure; to appear in General Relativity and Gravitatio

A novel photocatalytic conversion of Tryptophan to Kynurenine using black light as a light source

The photocatalytic conversion of an aqueous solution of l-tryptophan (Trp) to kynurenine (KN) was investigated under the illumination of different light sources. Results show that Trp converted to KN with a selectivity of 64% under the illumination of a medium pressure (MP) Hg lamp. KN selectivity was increased to >90% when black light (BL) was used a light source. The novel use of BL in the photocatalytic conversion of Trp to KN significantly reduces the energy consumption compared with MP ligh