Recently in Theoretical physics Category

In 1805 Thomas Young derived the relationship between the static forces of a liquid droplet at rest on a solid substrate. As shown in the schematic, the droplet’s contact angle, θ, can be determined by balancing the horizontal solid–liquid and solid–vapor forces and the horizontal component of the liquid–vapor force, determined by the surface tension, γ/v (see Physics Today, February 2007, page 84). However, for more than two centuries, theories yielded unrealistic singularities for stress and strain at the three-phase contact line. That’s because Young’s equation does not account for the vertical, out-of-plane force pulling on the solid substrate, which naturally should be balanced by the substrate’s elastic response. Now, researchers at Yale University and at consumer products manufacturer Unilever have experimentally and theoretically resolved the out-of-plane contributions. Using a confocal fluorescence microscope, the researchers, led by Yale’s Eric Dufresne, laced a 20-micron-thick film of silicone gel with fluorescent beads and measured the deformation due to a water droplet. At equilibrium, a one-micron-high ridge, illustrated in the inset, formed in the gel at the contact line. When the researchers factored the gel’s surface tension and thickness into a linear elastic model, they arrived at a nonsingular theoretical solution for stress that closely fit their experimental data. Their model, however, underestimates the deformations in the solid-liquid contact plane, which they believe are caused by pinning or viscous drag. (E. Jerison et al., Phys. Rev. Lett., in press.)—Jermey N. A. Matthews

In three dimensions, exchanging identical particles has a simple effect on a wavefunction: no change for bosons, multiplication by −1 for fermions. In two dimensions, things are more complicated. Consider the two ways to switch identical particles “A” and “B” shown in the figure. Because the clockwise and counterclockwise switches can’t be continuously deformed into each other, 2D exchange doesn’t just swap coordinates; it also involves a topological component. When many particles are involved, the topological issues are correspondingly more complex, and exchange operations might not commute. In that case the particles are said to have non-abelian (that is, noncommuting) anyon statistics. Non-abelian anyons are more than a mathematical curiosity: Condensed-matter physicists have plausibly argued that the quasiparticles that participate in the so-called ν = ⁵⁄₂ fractional quantum Hall state are objects of that type (see the article by Sankar Das Sarma, Michael Freedman, and Chetan Nayak in Physics Today, July 2006, page 32) . Now, Nayak (Microsoft Station Q and the University of California, Santa Barbara) and colleagues have, in the first calculation of its kind, explicitly demonstrated the compatibility of a specific popular candidate ν = ⁵⁄₂ wavefunction with non-abelian anyon statistics. The key step, says MIT’s Frank Wilczek, was to map the wavefunction to a rather different physical system amenable to attack with a well-established battery of mathematical tools. Does the wavefunction studied by the Nayak team actually describe the ν = ⁵⁄₂ state? That ball is in the experimentalists’ court. (P. Bonderson et al., Phys. Rev. B 83, 075303, 2011.)—Steven K. Blau

An ecosystem is a dynamic, complex tangle of predators and prey in which the depletion of one species can trigger a cascade that leads to the extinction of several others. Some cascades are structural—they propagate when an extinction leaves some predators with no prey. Others are dynamic—they occur when an initial extinction leaves the system in an unstable state that, in mathematical parlance, is drawn by an attractor toward multispecies extinction, even though more favorable steady states might exist. Now, simulations by Adilson Motter and Sagar Sahasrabudhe (both at Northwestern University) suggest that many dynamic cascades can be mitigated with the strategic removal or suppression of a second species. Some rescues are intuitive, such as removing a second species that’s a predator or prey of the first. But the ideal rescue species need not share such a direct link with the cascade-instigating species; it can even be a species that would have gone extinct in the cascade anyway. Sometimes just partial suppression of a species can spare the entire food web. The team demonstrated how its approach might work in the Coachella Valley ecosystem, depicted as a network in the figure. Arrows point from each prey to its predator. The larger circles indicate species that, if removed, would most likely instigate a cascade; the yellow circles, those most likely to mitigate one. The results suggest that smart, sometimes counterintuitive population-control measures could be instrumental in conserving ecosystems. (S. Sahasrabudhe, A. E. Motter, Nat. Commun. 2, 170, 2011.)—Ashley G. Smart

To a significant extent, the cells, tissues, organs, and so forth that make up a living organism act independently as they perform their related tasks. According to spin-glass models of evolution, modular structures analogous to those in biological systems generically arise for systems in changing environments. Moreover, such structures help ensure that a system is better able to cope with changes to come. Now Michael Deem of Rice University and his student Jiankui He have applied those conclusions to global trade. To do so, they came up with a parameter—the cophenetic correlation coefficient—that quantifies the modularity of the global trade network. As the figure shows, the system becomes more modular (the CCC increases) in response to environmental change—in this case, global recession. (The red bars indicate more severe recessions; the green bars, less severe. Data for the 2008 recession were not available.) But the overall trend during the past 40 years has been a mostly steady decline in the CCC as insular trade blocs—the modules—dissolved in favor of freer trade. According to evolution theory, and in contrast to much current economic thinking, the decreasing modularity implies that the global trade network is becoming less resistant to recessionary shocks such as a 1% dip in the US gross domestic product. And indeed, looking back at US recessions that have occurred during the past 30 years, Deem and He find that the most recent ones have had the greatest and longest lasting global impact. (J. He, M. W. Deem, Phys. Rev. Lett. 105, 198701, 2010.)—Steven K. Blau

There’s no reason to think that the lengthening of time predicted by the theory of relativity does not hold even for everyday speeds, but the effect is so minuscule that it has taken two of the world’s most accurate optical clocks to measure it. Trapped at the heart of each clock is an aluminum ion: Displacing the ion in one clock just slightly from the trap’s center induces a relative average speed difference between the two clocks’ ions of 10 m/s (22 mile/hr). The resulting fractional frequency difference is on the order of 10⁻¹⁶. That small shift was measured recently by James Chin-Wen Chou and his colleagues at NIST in Boulder, Colorado, using NIST’s newest optical clock, whose accuracy is 8.6 x 10⁻¹⁸, and a slightly less accurate older clock. The group also measured the frequency difference between the clocks’ ions when one clock was raised by 33 cm relative to the other. The measurements not only demonstrate the high performance reached by optical clocks but also show that they may play an important role in geodesy, the measurement of Earth’s gravitational potential. The time keepers might be sensitive to elevation changes as small as 1 cm if they can attain the current goal of 10⁻¹⁸ accuracy. Such measurements would complement those of satellite-borne instruments, which also have 1-cm sensitivity but average over large areas of Earth’s surface. (C. W. Chou et al., Science 329, 1630, 2010.)—Barbara Goss Levi

As famously predicted by Hendrik Casimir in 1948, parallel conductors in a vacuum will attract each other because the conductors impose boundary conditions that affect the vacuum energy of the electromagnetic field (see the article by Steve Lamoreaux in Physics Today, February 2007, page 40). In general, the Casimir force depends on the shape of the conductors and its value is notoriously difficult to calculate, but research groups worldwide have been developing increasingly applicable computational techniques. Now a team at MIT has shown how tabletop measurements might provide the key information needed for the general calculation. The Casimir force may be expressed as an integral over frequency (ω) of correlation functions that involve electric and magnetic fields. In principle, those frequency-dependent correlations can be obtained in a suitably scaled tabletop experiment from measurements of how an antenna at one point responds to a current generated at a distant point. In practice, such measurements won’t work because the integrand oscillates wildly with ω. The integrand becomes well behaved—it decays and doesn’t oscillate—if the integration is performed in the complex plane, but real antennas respond to real frequencies. The key observation made by the MIT team is that their mathematical expressions always involve ω in the combination εω², where ε is the permittivity. Thus, the researchers predict, a force integral with real vacuum permittivity and complex contour can be calculated from a tractable number of antenna measurements made at real ω in a medium of complex permittivity—for example, salt water. (A. W. Rodriguez et al., Proc. Natl. Acad. Sci. USA, in press, doi:10.1073/pnas.1003894107.)—Steven K. Blau

Among its marvelous consequences, general relativity asserts that a stationary clock at Earth’s surface will run slower than one high in a tower where the gravitational potential is weaker; the phenomenon is called gravitational redshift (see the article by Neil Ashby, Physics Today, May 2002, page 41). Now Holger Müller (University of California, Berkeley and Lawrence Berkeley National Laboratory) and colleagues report that the redshift idea, first experimentally confirmed 45 years ago, has passed its strictest test yet. In its analysis, the group reanalyzed a 10-year-old experiment that used atom interferometry to determine the gravitational acceleration. In that earlier work, an upward-directed atom interacted with a pair of laser pulses that put it in a superposition of states with differing momentum. As the figure shows, the phase of the atomic wavefunction evolves along each of the two paths, but with a lower frequency along the bottom path. A second pair of pulses tweaked the atom so that the diverging paths would reconverge; an experimental measurement of the probability that the atom is observed at the convergence point yields the phase difference between the two paths. As Müller and company discuss, the earlier-measured phase difference receives contributions due to the relative motion of the atom in its different states and from the laser interactions, but the two effects cancel. The total phase difference is attributable to the redshift. And to better than one part in 10⁸, it is precisely what is predicted by general relativity. (H. Müller, A. Peters, S. Chu, Nature 463, 926, 2010.) —Steven K. Blau

Natural light fields are threaded by lines of darkness. For monochromatic light, the phenomenon is familiar in laser speckle—the black points that appear in scattered light because of destructive interference. Those points, known as optical vortices, become lines in three dimensions; when multiple plane waves interfere, the vortices can form a complicated tangle throughout the volume of the light field. Using techniques from mathematics and optical wavefront engineering, Mark Dennis (University of Bristol), Miles Padgett (University of Glasgow), and their UK colleagues have now demonstrated that those lines of zero intensity can be shaped into linked loops and knots. The trick lay in finding the exotic solutions to Maxwell’s equations—or more precisely, the paraxial wave equation—that do the job. Last year Dennis and student Robert King realized they could exploit a topological technique known as Milnor mapping to construct a complex scalar function for a knot. To imprint the function into an optical field, Padgett and students Kevin O’Holleran and Barry Jack used a diffractive hologram to generate the proper destructive interference pattern onto an incoming laser beam. They spatially mapped out the resulting knot (shown here red) by measuring where the phases (different colors in the cross section) become singularities. One goal of the research is to better understand the role knotted vortices may play in systems as diverse as cold turbulent superfluids and hot magnetized plasmas. (M. R. Dennis et al., Nat. Phys. 6, 118, 2010.)—R. Mark Wilson

Unlike the branches of a tree, the network of veins in a typical leaf is full of closed loops. Even after a visit by a hungry insect, no part of the leaf is cut off from the network, as shown in the top part of the figure. But is a leaf’s fractal-like form, with loops of various sizes, the best possible network for resisting that type of damage, or might a different loop-filled structure be better? And is the hierarchical structure the optimum for any other criterion? Marcelo Magnasco (the Rockefeller University, New York) and colleagues sought to find out. Using a mathematical model that assigns each vein segment a cost proportional to its capacity raised to a power γ, they looked for the networks with a given total cost that suffered the least average strain under two sets of circumstances. First, they looked at damage to a randomly chosen vein segment. Second, they considered the case of a fluctuating load, in which the amount of fluid to be delivered to each part of the network varied in time and space. (Real leaves do sometimes need to handle fluctuating loads. So, more obviously, do most human-built networks.) They found that for low values of γ (results for γ = 0.1 are shown in the figure), both cases yielded hierarchical networks of loops, qualitatively similar to real leaves. (E. Katifori, G. J. Szöllősi, M. O. Magnasco, Phys. Rev. Lett., in press.) —Johanna Miller

Stretched out completely, a human chromosome would be several centimeters long. It is packed, along with its 45 companions, into a few-microns-wide cell nucleus in such a way that all the necessary genes are accessible to RNA transcription. Figuring out how that packing is done is no easy task. Microscopy helps, but provides nowhere near a complete picture. Now a research team led by Eric Lander of MIT and Job Dekker of the University of Massachusetts has developed a method for probing chromosomes’ folded structures. The researchers chemically join segments of a folded chromosome that are close in space, cut away and sequence the DNA around the crosslink, and compare those sequences to genome libraries to determine which parts of the chromosome are in contact. A matrix of the observed contacts, as shown in the figure, reveals large-scale organization. Analyzing the plaid pattern, the researchers found that most of the cell’s actively transcribed DNA was spatially segregated from most of the inactive DNA. On a smaller scale, chromosome segments a millimeter or so in extended length appeared to form so-called fractal globules with self-similar structures very different from that of a tangled polymer in equilibrium. So far, the researchers have studied only cultured cell lines: one derived from a tumor and another modified by a virus. They hope to apply their method to healthy cells and to look for differences in chromosome structure among cells of different types. (E. Lieberman-Aiden et al., Science 326, 289, 2009.) —Johanna Miller

Today's best fundamental theories—whether for gravity, electrodynamics, or elementary particles—say that the laws of physics are identical for all inertial observers, independent of their speed or direction of motion. That so-called local Lorentz invariance has been well tested for quantum field theories (see Physics Today, July 2004, page 40). To date, however, the LLI of gravitational interactions has received little attention, mostly because the weakness of gravity requires exquisitely sensitive experiments. In general, LLI tests are examined within the "standard model extension," which incorporates a series of coefficients, nine of which reflect gravitational effects. Any nonzero coefficients demonstrate violations of LLI and could reveal clues about quantum gravity, variants on general relativity, or other physics beyond the standard model. Some previously undetermined coefficients have now been pinned down by Holger Müller of the University of California, Berkeley, and his colleagues. Using an atom interferometer with an atomic fountain, they looked for anomalous variations in the gravitational acceleration g as Earth revolves through space. The physicists combined new results with those from previous experimental runs and with lunar-ranging data (see Physics Today, May 1996, page 26). The bottom line? Of the nine independent gravitational coefficients, five are now known to be zero to within parts per billion, and three to parts per million. One remains undetermined. The team also established that further improvements can come from using horizontal devices—perhaps guided atoms. (K.-Y. Chung et al., Phys. Rev. D 80, 016002, 2009.) —Stephen G. Benka

Synchronized oscillatory processes in populations of living cells can arise in two ways. In one type of transition, individual cells oscillate out of synchrony at low number density and gradually synchronize as their density is increased. In another type, cells exhibit no oscillations at low density, but above a threshold density they suddenly begin oscillating in synchrony. Biological systems' complexity makes understanding the transition mechanisms a challenge. But now, researchers led by Kenneth Showalter of West Virginia University have observed transitions of both types in a simpler nonbiological system. They used a version of the oscillating Belousov-Zhabotinsky reaction based on the catalyst ferroin, which they loaded onto porous particles 200 µm in diameter. When the particles were suspended in a reagent solution, the reaction on each particle oscillated at its own frequency, which could be monitored as the ferroin changed in color. Stirring the solution caused chemicals to be exchanged between each particle and the surrounding solution; as a result, the particles' oscillation cycles could influence one another and thereby synchronize, as shown in the time-sequence images in the figure. When the researchers stirred the solution slowly, they observed synchronization of the first, gradual type. When they stirred more quickly, the transition was of the second, sudden type. The researchers explain their results using a kinetic model of the reaction and species exchange, which may aid in the understanding of biological synchronization. (A. F. Taylor et al., Science 323, 614, 2009.) — Johanna L. Miller

In an emptying bathtub, water forms a whirlpool around the drain. But circular flow can’t persist to the very center of the vortex; there must be a water-free funnel. In 1985 Wojciech Zurek, following on work of Tom Kibble, suggested that “topological defects” analogous to the whirlpool could be generated spontaneously in a system undergoing a second-order phase transition. For a fast enough process in a large enough system, small regions independently change state, being unable to communicate with other, relatively far off regions. That independence allows parameters such as the quantum-mechanical phase angle to arrange themselves in vortex structures. Researchers have seen spontaneous vortex formation in, for example, superfluid helium-3, nonlinear optical systems, and superconductors (see the article by Kibble, PHYSICS TODAY, September 2007, page 47). Now a new system can be added to the list: the Bose–Einstein condensate. Deliberately inducing a vortex in a BEC is nothing new, but recent joint experimental work at the University of Arizona and numerical work at the University of Queensland in Australia represents the first study of spontaneous vortex formation in that particularly clean system. In the experiment, Chad Weiler and colleagues tweaked standard procedures to maximize the chance of their observing spontaneously formed vortices. After a trapped atomic gas transitioned to a BEC over the course of a few seconds, the group removed the trapping potential and imaged the escaping condensate. The vortices are revealed by dark, zero-density spots in the figure; the rightmost image shows two vortices, the others a single vortex. Continuing experiment and simulation together, Weiler and colleagues hope, will shed light on the universality of spontaneous topological defect formation in phase transitions. (C. N. Weiler et al., Nature 455, 948, 2008.) — Steven K. Blau

Related links:

Bose Einstein Condensation Lab at the University of Arizona College of Optical Sciences

Centre for Quantum-Atom Optics at the University of Queensland

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

Theorists have long predicted that scattering materials, such as milk and white paint, contain transparent channels that light can pass right through. Ordinarily, very little of the light in an incident beam enters those so-called open channels, and the materials appear opaque. But it should be possible to create a shaped wave that couples more light into the open channels. In fact, Ivo Vellekoop and Allard Mosk of the University of Twente in the Netherlands have done just that. Last year, they demonstrated a method for shaping a light wave, by tuning the relative phases of segments of their beam, so that much of the light transmitted through their scattering sample would be focused to a point. (See PHYSICS TODAY, October 2007, page 26.) Now, using the same algorithm with an improved apparatus, they’ve shown that they can increase the total amount of light passing through the material by as much as 44%. However, their device’s performance is still limited by tiny drifts of the sample with respect to the beam. Extrapolating from their results, they confirmed the theory’s prediction that if they could implement their algorithm perfectly, about two thirds of the incident light would be transmitted, regardless of the thickness of the scattering material. (I. M. Vellekoop, A. P. Mosk, Phys. Rev. Lett., in press.) — Johanna L. Miller

Visible light coming from the Sun pours down daily and is reflected back from Earth's surface as IR radiation. Extra warming occurs when some of that IR is absorbed and retained in the atmosphere. Only a trace gas in the atmosphere, CO2 is far outnumbered by O2 and N2 molecules, but its growing presence (mostly due to human activity) and its ability to absorb and trap IR radiation are thought to be instrumental in producing greenhouse effects. The interactions between atoms in a single molecule generate the molecule's dipole moment and polarizability, two properties that greatly affect how the molecule absorbs or scatters radiation. Going to the next level of complexity, a new study shows in detail how a large class of molecules, including CO2, absorbs and sometimes scatters light energy during intermolecular collisions. Michael Chrysos and his colleagues at the University of Angers (France) and Saint Petersburg State University (Russia) have derived exact mathematical formulas that can be used to calculate how collisions between so-called linear-rotor molecules modify the molecules' absorption spectra. During a molecular interaction, a transient supermolecular complex arises with its own degrees of freedom—distinct from those of the constituent molecules—and its own dipole moment or polarizability. The net result is that a broad band of frequencies, including many that are unavailable to single molecules, can be absorbed or scattered. The new study is important for several reasons: It allows exact calculations of how the intercepted IR photon energy is converted to kinetic energy and shared among neighboring gas molecules; it allows for the inclusion of higher-order effects, such as the simultaneous collision of three molecules; and it provides evidence that long-range intermolecular interactions are far more important than short-range ones for absorption, a conclusion in conflict with mainstream assumptions. (M. Chrysos et al., Phys. Rev. Lett. 100, 133007, 2008 [SPIN].) — Phillip F. Schewe