Recently in Theory & mathematical physics Category

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