Elemental Discoveries

by David Bradley

Waves in motion

Over the last two decades, the study of nonlinear wave propagation in solids has been recognised as one of the most fundamental and important phenomena from both a theoretical and a practical perspective. Mathematical, physical and numerical approaches have been applied to such studies in areas as diverse as waves in active or dissipative elastic media electroelastic and magnetoelastic media, waveguides. Moreover, the advent of high-performance computing has brought new power to researchers in this field.
  'They are paradigmatic for the understanding and implementation of efficient methods of applied mathematics, and also a source of innovative methods,' so say the guest editors of a special issue of Wave Motion, which reports the details of work presented to the 4th ICIAM (International Congress on Industrial and Applied Mathematics) in Edinburgh, Scotland, 5-9 July, 1999. The research discussed covers the latest developments in highly dispersive mechanisms, the presence of material inhomogeneities in the path of propagation, and quasi 1D or truly 2D systems.
  Yibin Fu and Sandra Hill of the Department of Mathematics, at the University of Keele, in Staffordshire, England, for instance presented results describing their analyses of nonlinear travelling waves in a coated elastic half-space which models the structures in a number of important applications, ranging from seismology, thin-film deposition, to the design and development of surface acoustic wave devices that perform nonlinear signal processing operations in electronic devices. They found that when the material properties of the coating are close to those of the underlying half-space, the structure supports a rich variety of multiple-mode travelling wave solutions, in contrast with other situations where travelling waves are predominantly monochromatic.
  The subject of shear waves in micro-faulted materials was covered by Paulo Cermelli and Franco Pastrone of the Department of Mathematics at the University of Turin, Italy, which could help seismologists understand how energy is dissipated during an earthquake.
  Pastrone and Cermelli have extended previous one- and two-dimensional models to a three-dimensional setting. The idea being to model microscopic faults by means of a microstructural parameter subject to its own micro-force balance. Variations are triggered when stress hits a threshold value and should lead to either energy dissipation during shearing, of rock for instance, or an energy exchange takes place leading to an amplification of macroscopic deformation. This is a situation that could be of some interest in interpreting the amplification of seismic waves which travel in some regions of the earth's crust says the team. An analysis of microseisms shows that they cannot be generated solely by external sources that trigger the release of "locked-in" internal energy. 'In our model,' explains Pastrone, 'this mechanism is explained by means of microstructures which can release energy, when a propagating wave is considered as an external source and the wave itself may be amplified.' The internal structure of the earth's crust is usually assumed to be dispersive because of its viscosity, so that the amplitude of a wave decays but data show amplification of seismic waves.
  Our final highlight from this issue revolves around the classical problem that wave theories usually describe solids as homogeneous materials. Homogeneity is not a precise enough description for modern physics and technology, however, according to Wave Motion Editor Gérard Maugin of the Pierre and Marie Curie University in Paris and colleagues Andrus Salupere and Jüri Engelbrecht of the Tallinn Technical University, in Estonia. When short wavelengths, coupled fields, phase changes, and other phenomena are involved in a study then the microstructure of a solid also has to be taken into account to provide useful results.
  The team has used a Korteweg-de Vries (KdV)-type nonlinear evolution equation to look closely at the effect of microstructure on nonlinear effects and found that they can be described by a quartic elastic potential and dispersive effects. The emerging equations should allow materials scientists to understand better the properties of martensitic-austenitic alloys and how solitons and solitary waves form within these materials.

Getting on top of CP violation

Physicists are inching towards answers to one of nature's best-kept secrets - the origin of mass and the reason why we live in a world of matter and not antimatter.
  Big Bang theory predicts that equal quantities of matter and its opposite number antimatter would have emerged from the cosmic fireball. But, we live in a world of matter and only observe antimatter in the likes of particle accelerators. Researchers have spent decades attempting to unlock the reasons behind this and believe that the clue lies in the violation of symmetry in nature.
  One such violation is that of charge conjugation combined with parity (CP) symmetry. If physicists could unravel CP violation, they might be able to learn why there is a dearth of antimatter. The problem facing them is that in more than three decades of intensive research only three examples of CP have been observed, in the decay of one particular entity, the K_L-meson, recently discovered evidence of differences between the B0 and anti-B0 decay to Psi K_S and in the very existence of the universe itself!
  David Atwood of Iowa State University, in Ames, USA, Shaouly Bar-Shalom of the INFN at the University of Rome, 'La Sapienza', Italy, Gad Eilam of the Technion-Institute of Technology, in Haifa, Israel and Amarjit Soni of the Brookhaven National Laboratory, in Upton, New York, recently reviewed the state of play and work by the team has led to a conclusion that should help physicists focus their efforts.
  According to the team, the effect of the standard model, which describes the strong interaction in terms of quarks and colour charge conservation and the electroweak interaction in terms of quarks, leptons and the Higgs boson is negligible in the hunt for CP violation since CP violation appears as a numerical parameter in the Standard Model but there is no obvious explanation as to where it comes from. Moreover, mechanisms of baryogenesis are purely theoretical at present because of the energy limitations of accelerators that would seek to create baryons and reveal CP violation in the process.
  Instead, the researchers suggest that the hunt for CP violation should focus on the top quark. The top quark, the team says, offers a unique system in which new CP-violations might be seen. If violation is observed in top quark reactions, this would be an 'unambiguous signal' of physics beyond the SM to shed light on baryogenesis and the physics of the early universe.
  The team reported their results in more detail in Phys. Rep., 2001, 347, 1-222.

Graphic by Bonnie Mackinnon of InkyBlue.com

Super World

The conference "Thirty Years of Supersymmetry", proceedings from which are published in a special issue of Nuclear Physics B (Proc Suppl, 101 (2001)) covers everything from the origins of the supersymmetry theory that hopes to unify matter and the forces that bind it together to the latest answers to tantalising questions such as why are some of the particles the theory requires missing from the physicist's repertoire and how and when can this supersymmetry be broken?
  Pierre Fayet of the Laboratory of Theoretical Physics at l'Ecole Normale Superieure in Paris discussed the origins of the minimal supersymmetric standard model. In the 1970s, Yuri Gol'fand and Evgeny Likhtman, Dmitry Volkov and Vladimir Akulov, and Julius Wess and Bruno Zumino took the first strident steps into the super world. Fayet muses that although the algebraic formulation of supersymmetry might at first glance relate the half-spin fermionic particles with their integral and forceful counterparts the bosons. But, he wonders whether we might have failed to observe directly even half of the particles necessary to complete the theory. If that is the case, then it will take a great deal more effort to allow supersymmetry to unify Forces and Matter.
  While the theorists were creating the theory of supersymmetry in the 1970s, Caltech's John Schwarz was introducing physics to string theory, in which particles are treated as one- dimensional strings rather than zero-dimensional points. At the conference reported, Schwarz described how string theory might one-day offer an explanation as to the origin of supersymmetry providing several key issues can be addressed. The original model devised by Pierre Ramond, Andre Neveu and Schwarz - the RNS model - obscured the essence of supersymmetry because it required a 26-dimensional spacetime and a tachyon to work. The more recent model devised by Green and Schwarz, however, makes the spacetime supersymmetry manifest.
  Schwarz' colleague Ramond also described how he has taken the stringy path to supersymmetry. In building such a theory, Ramond emphasises the importance of confusing bosons with fermions in 9+1 dimensions while pointing out the kinship of these particle classes is subtler in eleven dimensions.
  'The biggest complaint about string theory is that it does not offer concrete tests,' laments Keith Olive of the University of Minnesota, who organised the conference, 'but it does generates a consistent framework for unifying gravity with the other fundamental interactions.' Thirty years on, the untestable might still explain our super world.