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Two unusual physics papers have shot into the Top Ten, at #2 and #4. These
high fliers have already attracted more than 100 citations each. After a
rather slow start in 2006-07 these papers are soaring away as word spreads
about a powerful new technique for solving nonlinear equations described in
#2, while #4 examines ways of manipulating electromagnetic fields in order
to achieve invisibility.
Nonlinear differential equations are everywhere in physics. When confronted
by a nonlinear system, the theorist cannot express the variables as a sum
of independent components, which makes the finding of solutions rather
demanding. The weather, Einstein's field equations, magnetic fields in
solids, and shallow-water waves are all examples of nonlinear science. Such
systems produce startling phenomena: chaos, solitons, fractals, and more.
No general solutions exist that work for all nonlinear equations, which
means that each system must be studied as a separate problem, with
solutions emerging one by one. Numerical approximation techniques can help
in many situations, but in others the digital computation accumulates
rounding errors that push the solution off course. Finite element analysis
works well in engineering situations, but it uses a fixed grid of nodes
that is often not amenable to problems in fluid dynamics. Hot Paper #2
shows how a new analytical tool is solving what was hitherto unsolvable.
In 2000,
Ji-Huan
He (Donghua University, China) made a dramatic breakthrough by
introducing a new technique, the variational iteration method (VIM), which
he invented. Professor He is a rising star in computational science. His
paper #2, with Xu-Hong Wu as co-author, shows how to use VIM to reveal
soliton and compacton solutions to the nonlinear dispersion equations that
arise when studying the formation of drops in a stream of liquid. He's
group is motivated by a practical aspect: researching the production of
nanofibers by mimicking the spinning techniques of spiders.
Paper #2 is highly cited because it contains beautiful worked examples to
get analytical solutions to previously intractable nonlinear differential
equations that describe the behavior of real systems. Many of the citing
papers delight in showing how easy it is to use He's VIM across a wide area
of mathematical physics.
Hot Paper #4, with theorist Sir John Pendry
FRS1 (Imperial College,
London) as the lead author, is a tour de force on the control of
electromagnetic fields. In recent years Pendry's group has made impressive
strides in the production of metamaterials that can be used to manipulate
electromagnetic behavior. In classical physics the behavior of light, for
example, is controlled via the surface geometry of lenses and mirrors. Once
light has crossed a surface and entered the uniform glass of a lens, no
further change takes place until it exits at another surface. The science
of metamaterials is about engineering their internal structure so that an
electromagnetic wave is manipulated as it passes through an inhomogeneous
medium.
These new materials are engineered on a length scale that is intermediate
between atoms and the wavelength of the radiation being controlled. A large
range of electromagnetic responses can be controlled. Essentially anything
that does not violate Maxwell's equations can now be tailored, in
principle, with metamaterials.
Pendry and his colleagues show in #4 how electromagnetic fields can now be
redirected at will. In the case of controlling light, the introduction of a
gradient in the refractive index of the material allows the formation of
lenses and optical elements. The report shows how the unfrequented control
over refractive index that is now available alters the methodology of
electromagnetic design. The three conserved aspects of an electromagnetic
field can be controlled, which means that the fields can be made to flow
around objects like a fluid, returning to their original trajectories. The
principle being invoked is an exact manipulation of Maxwell's equations,
achieved with metamaterials.
As a worked example, #4 shows how electromagnetic fields could be
manipulated to conceal an object so that observers will be unaware that
something has been hidden from them. This is done by continuously altering
the permittivity and permeability of material surrounding the object so
that electromagnetic waves flow smoothly around it. So maybe Harry Potter's
invisibility cloak is not breaking the laws of physics!
Dr. Simon Mitton is a Fellow of St. Edmund’s College,
Cambridge, U.K.
Featured ScienceWatch.com podcast:
Professor Sir John Pendry, Chair in Theoretical Solid State
Physics at The Imperial College, London, discusses his work with magnetism
from conductors and enhanced nonlinear phenomena. Pendry has a
corresponding
Emerging Research Front Comment from October 2007
regarding this research. He is a
Current Classics scientist (Eng.) from
Feb.
&
Apr.
2008. Listen to podcast:
MP3|
WMA.