WHAT'S HOT IN... PHYSICS , July/August 2008

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.

Related information:

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.

Keywords: variable iteration method, VIM, Ji-Huan He, Spergel, nonlinear equations, chaos, solitons, fractals, John Pendry, electromagnetic fields, metamaterials, invisibility.