Elemental Discoveries

June 2001, Issue 42 by David Bradley

Gambling on tough turbulence

An answer to one of the toughest problems in understanding the turbulent movement of fluids may finally have gelled, according to results published recently in Physica A.
  Mathematician Christian Beck of Queen Mary and Westfield College, London has demonstrated the agreement between one theory of the strongest kind of turbulent flow - fully developed turbulence - and the experimental results, which could help explain countless natural from the flow of electrons in a high-energy plasma to the velocities of galaxies.
  Many phenomena behave like 'fluid' materials but don't stick to the rules of ordinary statistical mechanics. Instead, they and other systems such as cosmic rays, turbulence, financial data, a vibrating bed of powder, show non-Gaussian motion, behave as fractals, and have long-range correlations. 'Phenomena as diverse as the probability distribution of particles produced in a collider experiment, anomalous diffusion of cells in physiological solutions, even the distribution of citations of scientific articles, all behave in this way,' explains Christian Beck of Queen Mary and Westfield College.
  Beck has analysed the statistics surrounding the flow of turbulent fluids to calculate the energy properties of a flowing liquid. He has found that if he uses the Boltzmann-Gibbs entropy concept developed in the nineteenth century he cannot explain the anomalous behaviour. However, when the more general Tsallis entropies - a concept first thought of in 1985 by Constantino Tsallis of the Brazilian Center for Physical Research in Rio de Janeiro during a workshop coffee break - are used Beck can replicate precise experimental values for turbulent flow. 'Using the Tsallis entropies one gets precise coincidence of experimental and theoretical probability distributions,' explains Beck, 'with BG one does not.'
  In Beck's approach, every parameter is calculated using natural assumptions on the statistical behaviour of the turbulent flow. It is this point that allows such exact matching with the experimental values. Tsallis himself is very enthusiastic about Beck's results, 'It is an ideal theory in the sense that he calculates everything (including the uneasy entropic index q) from the experimental choices for the measures,' he told PD, 'And, when compared with the experimental results, the agreement is just great!'
  Seemingly unrelated phenomena, such as the turbulent motion of stock-market prices and horse-racing results might also succumb probabilistically speaking to the approach. 'The new formalism can in principle be used to better calculate the probability of losing (or gaining) money if you buy shares,' muses Beck. The formalism has ubiquitous applications,' adds Tsallis, ' for many complex phenomena related to power-law, as opposed to exponential, effects.' Whether or not the approach would lead to a profit is an open question for the tax inspector.

Feel the flow with Turbulence in Fluids by Marcel Lesieur

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Elemental Discoveries
June 2001, Issue 42

A little bit of Higgs

More clues on whether or not the Higgs boson exists have been found by CERN scientists have been published on PD. The Higgs boson is an elusive sub-atomic particle that is thought to explain the origin of mass. But, its existence, which first emerged from the work of Peter Higgs in Edinburgh in 1966 and later the Glashow-Weinberg-Salam (GWS) theory to explain what 'carries' the electroweak force, is yet to be proven.
  Two papers that provide the latest evidence for the Higgs boson - an unstable particle are now in press at Phys Lett B. The first is by the ALEPH Collaboration's 300-plus physicists. The ALEPH collaborators have analysed a data sample collected from the LEP at mass energies up to an incredibly high 209 GeV. They observed a signal more than three standard deviations above the expected background level. They believe this is consistent with the production of the Higgs boson with a mass close to 114 GeV/c2.
  The second paper is from the L3 Consortium. The scientists analysed LEP data from CERN and looked at the collisions of electrons and positrons at energies up to the same as those analysed by the ALEPH scientists. The various particle events hint that at the highest accessible Higgs masses there is a hint of a signal for this still elusive particle.
  Higgs bosons are thought to exist as a sea of particles pervading the universe and causing 'drag' on other particles, such as protons and electrons. This drag reveals itself as mass. David Miller of University College London has described the concept as 'In order to give particles mass, a background field is invented which becomes locally distorted whenever a particle moves through it.'
  The publication of these latest results comes just months after CERN announced its atom-smashing Large Electron Positron (Lep) collider would close. Funds released from the closure are destined for studies of the Higgs boson at the LHP which will begin work in 2006, irrespective of which centre - CERN or Fermilab's Tevatron Collider in Chicago - makes the final discovery.
  'Although the clues at LEP are very exciting, the excess is not significant enough to make any strong claims and could possibly be the result of a statistical fluctuation,' explains ALEPH's Higgs' group convenor Tom Greening, On the other hand, this mass is right at the edge of the LEP sensitivity and is perfectly consistent with a Higgs boson with a mass of about 115 GeV/c2. The final confirmation of Higgs is not likely to happen for some time yet. Fermilab will begin Run 2 of the Tevatron collider in March 2001 but from 2006 LHC will be sensitive to a Higgs boson up to 1000 GeV/c2. 'It will likely take many years for them to discover the Higgs boson and who the winner will be depends entirely on the mass of the Higgs boson,' adds Greening. They might even find it does not exist, at all. Find the Higgs source.

Learn more about CERN the birthplace of the Web in How the Web was Born: The Story of the World Wide Web by Robert Cailliau, James Gillies.

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Elemental Discoveries
June 2001, Issue 42

Getting to grips with butterflies

A fusion of mathematics and physics is helping physicists work on an old problem about why deterministic equations can lead to chaos. New equations emerging from the research might reduce the so-called 'butterfly effect' to a handful of equations and could be used to estimate the 'strength' of chaos in many-particle systems like models of solids and liquids.
  The problem of Hamiltonian mechanics stretches back to Newton's equations. 'All the dynamical systems in which energy is conserved, i.e., where dissipative effects, such as friction, can be ignored, such as a swinging pendulum, a mass sliding without friction, and the orbiting of the planets (ignoring tidal effects) are Hamiltonian,' explains Lapo Casetti of the Institute for Condensed Matter Physics, Florence, Italy.
  French mathematician Henri Poincaré realised that Newton's three- body problem - was another Hamiltonian example but that despite its deterministic description it behaved unpredictability - it was unstable. Poincaré, and later Cartan, failed to solve fully the problem. In the 1940s, Russian mathematical physicist Nikolaij Krylov showed that the exponential amplification of small deviations from the starting conditions could result in unstable behaviour in Hamiltonian systems. The concept entered the popular conscious as 'the butterfly effect'. Newton had become statistical.So, explain Casetti and his colleague Marco Pettini with E. G. D. Cohen of Rockefeller University, New York, [Physics Reports (2000, 337, 237- 341)] statistical mechanics might contribute to a solution to the chaos of Hamiltonian systems.
  The researchers have now taken the problem a stage further by looking at how the geometry of these chaotic systems relates to the curvature of the space in which movement takes place. They have now found an agreement between their equations and the outcome of computer simulations of models of many-particle systems, ranging from networks of coupled oscillators and rotators to models of classical field theories, such as the electromagnetic field.
  The subject is not closed, Casetti emphasises, the theory might still be improved. 'Hamiltonian systems are extremely important in physics because we believe all fundamental physical systems are Hamiltonian: dissipative effects are expected to be the consequence of a coarse-grained description (for example, when you describe a fluid in terms of a density and not the motion of the individual molecules),' he explains.
  The new equations will allow the Lyapunov exponent to be estimated. This value provides a measure of the strength of chaos and is related to the smallest timescale over which a system loses the memory of its initial conditions - it measures the power of the butterfly effect, in other words. The team hopes their equations will be useful in statistical mechanics and condensed matter physics allowing scientists to eliminate the usual extensive numerical simulations in many problems.
  The researchers also describe in the same paper how they have applied topological analysis to an important class of phase transitions and believe they have unearthed a new clue about their origin. The source of all the flapping

Find out more about chaos theory in Chaos: Making a New Science by James Gleick.

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Elemental Discoveries
June 2001, Issue 42

Moving cells

Statistics could be used to spot cancer cells, improve tissue engineering, or test wound-healing applications, according to an international team of physicists.
  A new way of looking at how cells move based on a statistical analysis could help researchers understand cell motion and help in characterizing cells of different types, function and viability. 'Possible long-term applications include diagnosis of cancerous cells,' explains Arpita Upadhyaya of the University of Notre Dame, Indiana, 'these may have different statistical properties compared to normal cells (since it is known that cancerous cells have impaired adhesive functions).'
  Biological processes such as morphogenesis in which cells change and move to alter the shape of an organ or the healing of wounds involve the movement of many individual cells or tissue masses from one part of the body to another. Such cell migrations also play a significant role in pattern formation such as giving the leopard its spots and the tiger catfish its stripes as well as the aggregation of amoebae and the collective motion of bacteria.
  Earlier studies have looked at how cells move when they are on an adhesive surface. But, Upadhyaya and colleagues at the Claude Bernard University in Lyon, France and Tohoku University, Japan, have taken a different approach to come up with a better analysis of cell motion. Many phenomena arise because 'fluid' materials, which can include aggregates of cells, do not adhere to the normal rules of statistical mechanics. Instead, such fluids and indeed many diverse phenomena from cosmic rays and turbulent liquids to financial results and vibrating powders, show non-Gaussian motion, behave as fractals, and have long-range correlations.
  Upadhyaya explains that typically studies of cell motion has relied on investigating non-interacting cells in well-defined surroundings in which normal diffusive motion is then observed, with Gaussian velocity distributions. However, cell motion in real living systems does not involve non-interacting cells on substrates, rather cells are driven by the formation of protrusions that probe the local environment, explains, Upadhyaya. These protrusions form through the polymerisation–deploymerisation of cytoskeletal actin filaments at the leading edge of the cell membrane. So, cellular movement depends very much on the local environment, neighbouring cells and reorganisation of the cell as it moves and develops.
  Upadhyaya says that little is known about the statistical mechanics of single cell motion in cellular aggregates and questions of whether the surroundings qualitatively affect the movement remain.
  She and her colleagues have now found a way to answer such questions, at least for the small multicellular organism - the freshwater polyp <I>Hydra viridissima</I>. Their results, however, provides a good general model of cellular development in general. They watched the changes in cell shape and position in aggregates using time-lapse transmitted light images of all cells in a particular field of view. It is, the researchers say, evident that several neighbouring cells in parts of the aggregate display highly correlated motion. This motion involves collections, or clusters of cells moving together and represents the first quantification of cell motion in aggregates. Make a move to Physica A

Investigate the world of fractals in Fractal Geometry of Nature by Benoit B. Mandelbrot.