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