Recently in Nonlinear science & chaos Category

Designers of transportation networks have to weigh the cost of serving customers against the need for an efficient, robust system. Natural organisms, too, confront tasks in which they need to balance competing desiderata. As it forages for food, for example, a slime mold must balance cost (that is, the amount of protoplasm it extrudes), efficiency, and the ability to withstand injury. Remarkably, as recently reported by Atsushi Tero and colleagues from Japan and the UK, the molds do as well as transportation engineers in balancing their analogous competing needs. Panel a of the figure re-creates a 17-cm-wide map of the principal cities served by the Tokyo railway system with a slime mold (yellow) at the location of Tokyo and food flakes (white) representing other cities. In about a day’s time, the slime mold finds where the nourishment is and generates a protoplasm network with the food flakes as nodes. Standard metrics for analyzing transportation networks reveal that the mold’s foraging network and the Tokyo railway system perform similarly. Perhaps more significantly, Tero and company imitated slime-mold networks in numerical simulations that don’t incorporate detailed biochemistry. Instead, they include a feedback step in which tubular links carrying a large protoplasm flux grow wider and flux-poor links contract. By tweaking their simulation parameters, the researchers could nudge the network toward, for example, greater cost efficiency. With optimal parameters, they could even improve upon the work of slime molds and human engineers. (A. Tero et al., Science 237, 439, 2010.) —Steven K. Blau

The phenomenon of dynamic stabilization can be demonstrated with an inverted pendulum: If the pivot point vibrates fast enough and strongly enough, the pendulum aligns with the vibration direction and can stably stand upside down, even at an angle, seeming to defy gravity. Physicists Greg Swift and Scott Backhaus (Los Alamos National Laboratory) looked at an analogous situation with gas in a so-called pulse tube that has one end much hotter than the other. Colder gas is denser and therefore sinks below the hotter gas; a vertical tube with the cold end down is like an undisturbed pendulum with the heavy bob at the bottom. However, raise the cold end above the hot end and convection sets in—the cold gas falls due to gravity and the hot gas rises in a natural convective flow. Such orientation-dependent effects are undesirable for cryogenic thermoacoustic pulse-tube refrigerators, like the commercial one shown here, in which the gas is used to transmit acoustic power but not heat. (For more on thermoacoustics, see Physics Today, July 1995, page 22.) Swift and Backhaus found that suppression of convection when these refrigerators run at high enough frequency and amplitude is related to the well-understood stabilization of the inverted pendulum. Although their experiments and theoretical analysis are beginning to unravel the essentially nonlinear physics at the core of the system, many mysteries remain, including the actual role of the oscillating pressure. (G. W. Swift, S. Backhaus, J. Acoust. Soc. Am. 126, 2273, 2009.) —Stephen G. Benka

Two-dimensional spectroscopy of materials, in its simplest form, measures the change in a sample’s interaction with radiation at one frequency caused by excitation at another. First used in nuclear magnetic resonance and later applied at IR and optical frequencies, the technique can separate overlapping peaks in a complicated spectrum or probe the flow of energy through systems such as the light-harvesting molecules involved in photosynthesis. (See Physics Today, July 2005, page 23.) In 2D Fourier-transform optical (FTOPT) spectroscopy, the sample is excited not with monochromatic light but with a pair of phase-related femtosecond pulses separated by a variable delay t₁; the time-domain data are transformed into a spectrum as a function of frequency ω₁. The second field is likewise replaced by a pair of phase-related pulses, one of which is a so-called local oscillator that allows the radiated field to be recorded as a function of time t₃ or frequency ω₃. Now, Keith Nelson and colleagues at MIT have produced 3D FTOPT spectra, in which the signal is a function of ω₁, ω₃, and also ω₂, corresponding to the time t₂ between the two pulse pairs. Applying their technique to semiconductor quantum wells—a system in which electrons are excited from nondegenerate valence-band states into the same conduction-band states—they found that important pathways whose signals were indistinguishable in a 2D spectrum could often be separated in a 3D spectrum. (D. B. Turner et al., J. Chem. Phys., in press.) —Johanna Miller

Ultrashort, ultraintense laser pulses undergo competing interactions: The nonlinear Kerr effect self-focuses the beam, while multiphoton ionization generates a plasma that defocuses the beam and prevents it from collapsing. The result is a self-channeled, nondiffracting beam with a tight core, termed a filament, consisting of the intense laser field and the generated plasma (see Physics Today, August 2001, page 17). Filaments emit broadband light in the forward direction and are self-healing, properties that yield a variety of applications, including remote atmospheric sensing and spectroscopy.
Recent work by Pavel Polynkin (University of Arizona), Demetrios Christodoulides (University of Central Florida), and colleagues has put a new twist on the filaments. Unlike earlier studies, which relied on Gaussian or other axially symmetric beam profiles, Polynkin and company used axially asymmetric beams: With a phase modulator, they shaped the transverse profile of their femtosecond pulses into the form of a two-dimensional Airy function. The resulting beams remained diffraction free, but their peak intensities followed a parabolic trajectory reminiscent of projectile motion. (Momentum was still conserved, however, thanks to the momentum of the other parts of the beam.) The figure shows the calculated plasma density that accompanies a 5-mJ Airy beam as its peak traces its parabolic path. The curvature could be controlled experimentally by changing the focal lengths of the lenses used. The forward emission from curved laser filaments could find use as a broadband, wide-angle illumination source for remote sensing and for laser-induced breakdown spectroscopy. (P. Polynkin et al., Science 324, 229, 2009.) — Richard J. Fitzgerald

To map molecules in cells and tissue, researchers prefer biomedical imaging techniques that rely solely on the intrinsic responses of chemical bonds to optical stimulation. Although fluorescence microscopy and other chemical tagging methods yield high-resolution images, they also introduce foreign species or synthetic derivatives that can alter the dynamics of intracellular processes. Spontaneous Raman scattering, which uses a single laser beam to excite the vibrational and rotational modes in chemical bonds, requires no chemical labels but generates a weak signal that gets muddled by Rayleigh scattering. A more sensitive technique known as coherent anti-Stokes Raman scattering uses multiple laser beams to generate coherent optical signals that enhance resonant frequencies in the sample; that method, however, also produces nonresonant background noise. Recently a team led by Harvard University chemist Sunney Xie demonstrated a new technique based on stimulated Raman scattering that tunes the difference between the frequencies of two laser beams to match a desired molecule's resonant frequency, thus amplifying the Raman signal. The measurable intensities of the transmitted beams change only when a match occurs; nonresonant signals are not picked up. The images show the top view (a) and the depth profile (b) of an acne medication (blue) that penetrated a mouse's skin, thus demonstrating the potential of the new technique to monitor drug delivery. (C. W. Freudiger et al., Science 322, 1857, 2008.)
— Jermey N. A. Matthews

Supercontinuum emission extends from the IR through the visible to the UV. As Robert Alfano and Stanley Shapiro discovered 40 years ago, one can generate supercontinuum pulses by sending bright, narrowband pulses through an optical fiber or other highly nonlinear material. Sometimes, depending on the noise, the process of a generating supercontinuum pulse also begets rare, intense pulses known as rogue waves. The artist's impression depicts the process. Ordinarily, rogue waves are sporadic and unpredictable, but if they could be produced to order, researchers would have access to bright, amplified pulses of supercontinuum light. UCLA's Daniel Solli, Claus Ropers, and Bahram Jalali have done just that, at least over a broad range in the IR. Their technique relies on sending in a second seed pulse right after the main pump pulse. The seed pulse is 10000 times weaker than the pump pulse and, with a central wavelength of 1630 nm, redshifted from the pump pulse by about 100 nm. Adjusting the relative timing of the two pulses has a dramatic effect. When timed optimally, the two pulses always generate a supercontinuum pulse of rogue-sized magnitude. What's more, the supercontinuum pulses are uniform in both intensity and spectrum. How does the technique work? Supercontinua begin from a nonlinear process called modulation instability, which produces lobes at either side of the pump pulse spectrum. In the presence of noise, the supercontinuum pulses can vary erratically from pulse to pulse, occasionally yielding a rogue wave. According to the UCLA team's numerical analysis, seed pulses tame the modulation instability and prompt the controllable formation of rogue waves. Data switching and routing in optical networks are among the applications the UCLA team envisions. (D. R. Solli, C. Ropers, B. Jalali, Phys. Rev. Lett. 101, 233902, 2008). — Charles Day

Soft biological tissue is often subjected to forces that affect the tissue’s geometry, and finite elasticity provides a robust theoretical framework for analyzing the mechanical behavior of those tissues. Although the theory can accommodate anisotropic, nonlinear, and inhomogeneous processes subjected to large stresses and strains, its complexity makes many problems intractable. For growing tissue, though, the slow addition of cells generates shape- or size-changing stresses that are small enough to model successfully (see PHYSICS TODAY, April 2007, page 20). So, too, are simple geometries for tissues in equilibrium, even after those tissues are subjected to large stresses. Two recent papers have looked at applying the theory to those cases in thin elastic disks. In one recent study, Julien Dervaux and Martine Ben Amar (both of École Normale Supérieure, Paris) looked at anisotropic growth rates: If growth was faster in the radial than in the circumferential direction, the disk became conelike, while a reversal of rates generated saddle shapes. A separate study by Jemal Guven (National Autonomous University of Mexico) along with Martin Müller (ENS) and Ben Amar looked at excessively large circumferences for a given radius. Using the fully nonlinear theory, the researchers found an infinity of quantized equilibrium states for an ever-increasing perimeter at fixed radius. The ripples around the edge grew in size and number—not unlike the flower petals shown here—eventually crowding together enough to touch, like the ruffled collar in a portrait by Rembrandt. For more on the elasticity of thin sheets, see the article in PHYSICS TODAY, February 2007, page 33. (J. Dervaux, M. Ben Amar, Phys. Rev. Lett. 101, 068101, 2008; M. M. Mueller, M. Ben Amar, J. Guven, Phys. Rev. Lett., in press.) — Stephen G. Benka

The recently elucidated crystal structure of a promising class of inorganic polymer salts reveals why these materials generate strong second-harmonic generation (SHG) responses to optical stimulation. In general, asymmetric inorganic polymer thin films with highly polarizable bonds exhibit strong nonlinear optical behavior, and are used in some tunable, coherent IR lasers to probe the electronic or structural properties of molecules or surfaces. A team from Northwestern University and Argonne National Laboratory used Argonne’s Advanced Photon Source to study the quaternary salts formed from the zirconium selenophosphate (ZrPSe₆^-) polyanion and its complementary metal cation (K⁺, Rb⁺, or Cs⁺)—this class of salt tends to crystallize as microneedles (see figure 1). The crystal structure (see schematic in figure 2) revealed a distortion in the molecular backbone from its ideal geometry, which contributes to the salt's high polarity. The second harmonic—a beam generated in the crystal and emitted at half the wavelength and twice the frequency of incident light—for the sample with the largest cation, Cs⁺, had an intensity 15 times that produced by a typical commercial nonlinear optical material. Even the smallest cation, K⁺, mixed with Cs⁺, produced about double the SHG response of the commercial benchmark material. The new salts exhibit strong photoluminescence in solution; they are also optically transparent from the mid- to the near-IR region, which gives them potential for use in a range of applications, from broadband communication to medical devices. (S. Banerjee et al., J. Amer. Chem. Soc. 130, 12270, 2008.) — Jermey N. A. Matthews

A ferrofluid is a colloidal suspension of nanometer-sized magnetic particles in a nonmagnetic carrier fluid. As you might expect, it can be easily manipulated with external magnetic fields and often exhibits different patterns and instabilities. For example, when a sufficiently strong magnetic field is applied perpendicular to the flat surface of a ferrofluid, the Rosensweig instability produces a stationary array of peaks protruding above the surface. When a similar field is applied to a ferrofluid droplet immersed in a confined immiscible liquid, the labyrinthine instability produces horizontal fingering as the two fluids interpenetrate. A new experiment reveals a hybrid situation in which those two normally distinct instabilities occur simultaneously. Scientists from Taiwan and Brazil immersed a ferrofluid droplet in a thin layer of a miscible nonmagnetic fluid. The images of the experiment, with a side view in the upper panels and a top view in the lower ones, show what the researchers found after switching on the field. The Rosensweig instability grows rapidly to its greatest amplitude in 0.43 s (left panels), at which time diffusion is already affecting the base of the droplet, decreasing the magnetic body force that sustains the peak against gravity and surface tension. At 1.2 s (middle panels), the peak is clearly decaying as the fingering progresses and after 5 s (right panels) the surface is again flat and radial diffusion dominates. (C.-Y. Chen, W.-K. Tsai, J. A. Miranda, Phys. Rev. E 77, 056306, 2008 [SPIN].)    — Stephen G. Benka