Research and Scholarly Activity

General relativity and geometry in physics

My main research activity is in general relativity. In particular, I'm interested in the causal and large-scale structure of space-time. This aspect of the structure of space-time is conformally invariant, and is intimately tied up with the light cones and light rays, or null geodesics in space-time. Much of my research has involved trying to understand the causal structure of space-time by considering the space of null geodesics, and structures on that space. I also work in other aspects of general relativity, and some areas of mathematics related to general relativity.

  • RJ Low (1989) The geometry of the space of null geodesics Journal of Mathematical Physics 30 809-811
  • RJ Low (1989) Apparent velocities in relativity theory European Journal of Physics 10 67-70
  • RJ Low (1990) Twistor linking and causal relations Classical and Quantum Gravity 7 177-187 LaTeX file
  • RJ Low (1990) Spaces of causal paths and naked singularities Classical and Quantum Gravity 7 943-954 LaTeX file
  • RJ Low (1990) The causal geometry of twistor space Journal of mathematical physics 31 863-867
  • RJ Low (1990) An acceleration-free version of the clock paradox European Journal of Physics 11 25-27
  • MS Madsen and RJ Low (1991) The stability of vacuum solutions in generalized gravity Physics Letters B241 207-210
  • RJ Low (1992) Topological changes in lower dimensions Classical and Quantum Gravity 9 L161-L165 LaTeX file
  • RJ Low (1993) Celestial spheres, light cones, and cuts Journal of Mathematical Physics 34 315-319 LaTeX file
  • RJ Low (1994) Twistor linking and causal relations in exterior Schwarzschild space Classical and Quantum Gravity 11 453-456 LaTeX file
  • RJ Low (1995) When moving clocks run fast European Journal of Physics 16 228-229 TeX file
  • RJ Low (1995) Time machines without closed causal geodesics Classical and Quantum Gravity 12 L37-L38 LaTeX file
  • RJ Low (1995) Comment on Singularity Theorems and the [General Relativity + Additional Matter Fields] Formulation of Metric Theories of Gravitation General Relativity and Gravitation 27 969-972 LaTeX and Bib files
  • JK Beem, RJ Low and PE Parker (1996) Spaces of Geodesics: products, coverings, connectedness. Geometriae Dedicata 59 51-64 TeX file
  • SG Harris and RJ Low (1995) Causality conditions and Hausdorff orbit spaces in spacetimes Geometry and Topology of Submanifolds, VII, Differential Geometry in honour of Prof. Katsumi Nomizu, Edited by F. Dillen and M. Magid and U. Simon and I Van de Woestijne and L Vestraelen, World Scientific Publishing Co AMSTex file
  • RJ Low (1998) Stable Singularities of Wave-Fronts in General Relativity Journal of Mathematical Physics 39 3332-3335 LaTeX file
  • T R Field and R J Low (1998) Causal relations via linking in twistor space Journal of Geometry and Physics 28 339-348 for a PostScript copy
  • R J Low (1999) Speed limits in general relativity Class. Quantum Grav. 16 543-549 LaTeX file
  • RJ Low (2000) The structure of cosmic strings Journal of Mathematical Physics 41 6364-6368 PostScript file
  • RJ Low (2000) Continuous causal representation of space-time via sphere orderings Journal of Mathematical Physics 41 6525-6528 LaTeX file
  • S G Harris and R J Low (2001) Causal monotonicity, omniscient foliations and the shape of space Class. Quantum Grav. 18 27--43 AMS-TeX file
  • R J Low (2001) The space of null geodesics Nonlinear Analysis 47 3005--3017 LaTeX file
  • R J Low (2002) Light sheets and the covariant entropy conjecture Class. Quantum Grav. 19 L1--L4 on gr-qc
  • R J Low (2005) The space of null geodesics (and a new causal boundary) Springer Lecture Notes in Physics 692 35--50 pdf file
  • R J Low (2007) The Red Queen visits Minkowski space European Journal of Physics 28 367--371 pdf file
  • RJ Low (2009) Comment on `A note on non-compact Cauchy surfaces' Classical and Quantum Gravity 26 128001 pdf file
  • RJ Low (2010) Simple connectedness of space-time in the path topology Classical and Quantum Gravity 27 107001 pdf file
  • RJ Low (2011) Electrodynamics, differential forms, and the method of images European Journal of Physics 27 1413--1417 pdf file
  • RJ Low (2011) Causality and Borromean linking in twistor space Classical and Quantum Gravity (to appear) pdf file
  • RJ Low (2011) Characterizing the causal automorphisms of 2-d Minkowski space Classical and Quantum Gravity (to appear) pdf file
  • RJ Low (2011) Framing curves in Euclidean and Minkowski space pdf file

There are numerous excellent web-sites on GR: a good place to start is with the relativity FAQ file.

Liquid crystals

More recently I have become involved in work on the numerical simulation of liquid crystals, in association with Prof Maureen Neal in the Faculty of Science and Engineering, Manchester Metropolitan University, and in statistical physics with a departmental colleague, Dr Ralph Kenna .

  • R J Low (2002) Measuring order and biaxiality Eur. J. Phys. 23 111--117 LaTeX or pdf with a couple of associated MATLAB functions, nemord.m and biaxial.m.
  • S J Johnston, R J Low, M P Neal (2002) Computer simulation of apolar bent-core and rodlike molecules Phys Rev E 65 051706
  • M Solymosi, RJ Low, M Grayson, MP Neal, MR Wilson, DJ Earl (2002) Scaled chiral indices for ferroelectric liquid crystals Ferroelectrics 277 169--176
  • M Solymosi, RJ Low, M Grayson, MP Neal (2002) A generalized scaling of a chiral index for molecules J Chem Phys 116 9875--9881
  • SJ Johnston, RJ Low, MP Neal (2002) Computer simulation of polar rod-like molecules Ferroelectrics 278 91--100
  • H Kamberaj, RJ Low, MP Neal (2003) Symplectic and time reversible integrator for rigid bodies. Systems Science 29 31--45
  • HJ Kamberaj, M Osipov, R Low, MP Neal (2004) Helical twisting power and chirality indices , Molecular Physics 102 431-446
  • HJ Kamberaj, R Low, MP Neal (2005) Molecular Structure and Helical Twisting Power Ferroelectrics 315 183--196
  • HJ Kamberaj, R Low, MP Neal (2005) Time reversible and symplectic integrators for molecular dynamics simulations of rigid molecules Journal of Chemical Physics 122 224114 (30 pages)
  • MP Neal, H Kamberaj and R Low (2005) Some calculations of molecular chirality Molecular Crystals and Liquid Crystals 439 1937-1943
  • H Kamberaj, RJ Low, MP Neal (2006) Correlation between molecular chirality and helical twisting power: a computer simulation study Molecular Physics 104 335-357
  • B Berche, C Chatelain, C Dhall, R Kenna, R Low, J-C Walter (2008) Extended scaling in high dimensions Journal of Statistical Mechanics P11010
  • EO Yewande, MP Neal, R Low (2009) The Hausdorff chirality measure and a proposed Hausdorff structure measure Molecular Physics 107 281--291

There are various sites which can provide you with information on liquid crytals. A useful starting point is the Virtual Textbook maintained by Case Western Reserve University. To find out what's currently going on in the world of liquid crystals, go to the Home page for the British Liquid Crystal Society.If you'd like to visit the site of one particular research group which specialises in molecular simulation, you might try the Bristol University Molecular Simulation Home Page.

Paedagogical and expository writings

As I also lecture/teach, I have some interest in producing paedagogical material. (Note that the Eur. J. Phys. papers listed above might just as well appear here.)

  • RJ Low (1989) Vector interpolation for surface normal calculation The Visual Computer 5 158-159
  • RJ Low (1990) On the solution of $\dot{\bf x}=A{\bf x}$ International Journal of Mathematical Education in Science and Technology 21 516-517
  • RJ Low (1991) The geometry of the Karnaugh map International Journal of Mathematical Education in Science and Technology 22 137-140 TeX file
  • RJ Low (1994) A classical conundrum, or, the importance of asking the right question International Journal of Mathematical Education in Science and Technology 25 314-315 TeX file
  • RJ Low (1994) Another look at complex differentiability International Journal of Mathematical Education in Science and Technology 25 469-470 TeX file
  • F Giannasi and RJ Low (1995) Introductory mathematics for computer science and information technology (Longman Higher Educational) There is a list of typos. If you see any not listed here, let me know and I'll add them.
  • RJ Low and AR Batchelor (1998) The relativistic shape of spherical wavefronts European Journal of Physics 19 133--136 TeX file
  • R J Low (1998) Coaxial Poiseuille flow as a general counter-example International Journal of Mathematical Education in Science and Technology 29 918--921
  • R J Low (2004) Waves, in Patterned Ground: entanglements of nature and culture ed S Harrison, S Pile, N Thrift (Reaktion Books)

Societies

There are a number of societies for those who are interested in mathematics, or involved with it professionally. I'm currently a member of the London Mathematical Society, and the Institute for Mathematics and its Applications.

LMS IMA

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