Broken symmetry.

Review of the book : Lucifer's legacy, the meaning of asymmetry, by F. Close, Oxford University Press, Oxford, UK

Symmetry-breaking in cumulative measures of shapes of polymer models.

Using numerical simulations we investigate shapes of random equilateral open and closed chains, one of the simplest models of freely fluctuating polymers in a solution. We are interested in the 3D density distribution of the modeled polymers where the polymers have been aligned with respect to their three principal axes of inertia. This type of approach was pioneered by Theodorou and Suter in 1985. While individual configurations of the modeled polymers are almost always nonsymmetric, the approach of Theodorou and Suter results in cumulative shapes that are highly symmetric. By taking advantage of asymmetries within the individual configurations, we modify the procedure of aligning independent configurations in a way that shows their asymmetry. This approach reveals, for example, that the 3D density distribution for linear polymers has a bean shape predicted theoretically by Kuhn. The symmetry-breaking approach reveals complementary information to the traditional, symmetrical, 3D density distributions originally introduced by Theodorou and Suter.

Magnetoelectricity in the ferrimagnetic Cu2OSeO3: symmetry analysis and Raman scattering study

sublattices ferrimagnet Cu2OSeO3 with a cubic symmetry and a linear magnetoelectric effect. There is no spectroscopic evidence for structural lattice distortions below T-C=60 K, which are expected due to magnetoelectric coupling. Using symmetry arguments we explain this observation by considering a special type of ferrimagnetic ground state which does not generate a spontaneous electric polarization. Interestingly, Raman scattering shows a strong increase of electric polarization of media through a dynamic magnetoelectric effect as a remarkable enhancement of the scattering intensity below T-C. New lines of purely magnetic origin have been detected in the magnetically ordered state. A part of them are attributed as scattering on exchange magnons. Using this observation and further symmetry considerations we argue for strong Dzyaloshinskii-Moriya interaction existing in the Cu2OSeO3. (c) 2010 American Institute of Physics. [doi:10.1063/1.3455808]

Bilateral symmetry of radial pulse in high-level tennis players: implications for the validity of central aortic pulse wave analysis.

BACKGROUND: Reconstruction of the central aortic pressure wave from the noninvasive recording of the radial pulse with applanation tonometry has become a standard tool in the field of hypertension. It is not presently known whether recording the radial pulse on the dominant or the nondominant side has any effect on such reconstruction. METHOD: We carried out radial applanation tonometry on both forearms in young, healthy, male volunteers, who were either sedentary (n = 11) or high-level tennis players (n = 10). The purpose of including tennis players was to investigate individuals with extreme asymmetry between the dominant and nondominant upper limb. RESULTS: In the sedentary individuals, forearm circumference and handgrip strength were slightly larger on the dominant (mean +/- SD respectively 27.9 +/- 1.5 cm and 53.8 +/- 10 kg) than on nondominant side (27.3 +/- 1.6 cm, P < 0.001 vs. dominant, and 52.1 +/- 11 kg, P = NS). In the tennis players, differences between sides were more conspicuous (forearm circumference: dominant 28.0 +/- 1.7 cm nondominant 26.4 +/- 1.5 cm, P < 0.001; handgrip strength 61.4 +/- 10.8 vs. 53.4 +/- 9.7 kg, P < 0.001). We found that in both sedentary individuals and tennis players, the radial pulse had identical shape on both sides and, consequently, the reconstructed central aortic pressure waveforms, as well as derived indices of central pulsatility, were not dependent on the side where applanation tonometry was carried out. CONCLUSION: Evidence from individuals with maximal asymmetry of dominant vs. nondominant upper limb indicates that laterality of measurement is not a methodological issue for central pulse wave analysis carried out with radial applanation tonometry.

Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Tight open knots.

The tightest open conformations of a few prime knots (3(1), 4(1), 5(1), 5(2), and 6(3)) found with the use of the SONO algorithm are presented and discussed. The conformations are obtained from the tightest closed conformations of the knots by cutting and opening them at different locations. The length of the rope engaged in each of the open conformations is calculated. The curvature and torsion profiles of the unique tightest conformations of the 3(1) and 4(1) open knots are presented and discussed. In particular, symmetry properties of the knots reflected within their curvature and torsion profiles are analysed. Connections with the physics of polymers are discussed.

Evaluation of the 3D symmetry of the knees when walking using na ambulatory inertia system: results 14 months after ACL Plasty.

Purpose of the study: Reconstruction of the anterior cruciate ligament (ACL) controls laxity but does not enable restoration of strictly normal 3D kinematics. The purpose of this study was to compare the kinematics of the pathological knee with that of the healthy knee after ACL plasty. This study applied a new ambulatory system using miniature captors. Material and method: Five patients with an isolated injury of the ACL participated in this study. The patients were assessed after injury (T1), at five months (T2), and at 14 months (T3) after surgery. The assessment included laxity (KT-1000), the IKDC score and the Lysholm score. The 3D angles of the knees were measured when walking 30 m on flat ground using a system composed of to small inertia units (3D accelerometer and 3D gyroscope) and a portable recorder. Functional settings were optimised and validating to ensure easy precise measurement of the 3D angles. Symmetry of the two knees was quantified using a symmetry index (SI) (difference in amplitude normalised in relation to mean amplitude) and the correlation coefficient CC. Results: Clinical indicators improved during the follow-up (IKDC T1: 3C, 2C; T2: 5B; T3: 2A, 3B; subjective IKD: 53-95; Lysholm 67-96). Mean laxity improved from 8.6m to 2.5 mm. The gait analysis showed increased symmetry in terms of amplitude for flexion-extension (SI: −17% at T1, −1% at T2, 1% at T3), and an increase in symmetry in terms of the rotation signature (CC: 0.16 at T1, 0.99 at T2, 0.99 at T3). There was no trend to varus-valgus. Discussion: This study demonstrates the clinical application of the new ambulatory system for measuring 3D angles of the knee joint. Joint symmetry increased after ACL plasty but still showed some perturbation at 14 months. The results observed here are in agreement with the literature. Other patients and other types of gait are being analysed. Conclusion: This portable system allows gait analysis outside the laboratory, before and after ACL injury. It is very useful for follow-up after surgery.

Geometry and physics of catenanes applied to the study of DNA replication.

The concept of ideal geometric configurations was recently applied to the classification and characterization of various knots. Different knots in their ideal form (i.e., the one requiring the shortest length of a constant-diameter tube to form a given knot) were shown to have an overall compactness proportional to the time-averaged compactness of thermally agitated knotted polymers forming corresponding knots. This was useful for predicting the relative speed of electrophoretic migration of different DNA knots. Here we characterize the ideal geometric configurations of catenanes (called links by mathematicians), i.e., closed curves in space that are topologically linked to each other. We demonstrate that the ideal configurations of different catenanes show interrelations very similar to those observed in the ideal configurations of knots. By analyzing literature data on electrophoretic separations of the torus-type of DNA catenanes with increasing complexity, we observed that their electrophoretic migration is roughly proportional to the overall compactness of ideal representations of the corresponding catenanes. This correlation does not apply, however, to electrophoretic migration of certain replication intermediates, believed up to now to represent the simplest torus-type catenanes. We propose, therefore, that freshly replicated circular DNA molecules, in addition to forming regular catenanes, may also form hemicatenanes.

Synchrotron-based X-ray tomographic microscopy for rock physics investigations

Synchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis of our data.