Breaking of symmetry in microfluidic propulsion driven by artificial cilia.

In this Brief Report we investigate biomimetic fluid propulsion due to an array of periodically beating artificial cilia. A generic model system is defined in which the effects of inertial fluid forces and the spatial, temporal, and orientational asymmetries of the ciliary motion can be individually controlled. We demonstrate that the so-far unexplored orientational asymmetry plays an important role in generating flow and that the flow increases sharply with Reynolds number and eventually becomes unidirectional. We introduce the concept of configurational symmetry that unifies the spatial, temporal, and orientational symmetries. The breaking of configurational symmetry leads to fluid propulsion in microfluidic channels.

On representing chemical environments

We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms, and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighbourhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbours increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether new approach, called Smooth Overlap of Atomic Positions (SOAP), that sidesteps these difficulties by directly defining the similarity between any two neighbourhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

Autonomous rigid body attitude synchronization

This paper studies some extensions to the decentralized attitude synchronization of identical rigid bodies. Considering fully actuated Euler equations, the communication links between the rigid bodies are limited and the available information is restricted to relative orientations and angular velocities. In particular, no leader nor external reference dictates the swarm's behavior. The control laws are derived using two classical approaches of nonlinear control - tracking and energy shaping. This leads to a comparison of two corresponding methods which are currently considered for distributed synchronization - consensus and stabilization of mechanical systems with symmetries. © 2007 IEEE.

Symmetry-extended counting rules for periodic frameworks.

A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators

Mode characteristics for two-dimensional equilateral-polygonal microresonators are investigated based on symmetry analysis and finite-difference time-domain numerical simulation. The symmetries of the resonators can be described by the point group C-Nv, accordingly, the confined modes in these resonators can be classified into irreducible representations of the point group C-Nv. Compared with circular resonators, the modes in equilateral-polygonal resonators have different characteristics due to the break of symmetries, such as the split of double-degenerate modes, high field intensity in the center region, and anomalous traveling-wave modes, which should be considered in the designs of the polygonal resonator microlasers or optical add-drop filters.

Investigation of mode characteristics for a square cavity with a pedestal by a three-dimensional finite-difference time-domain technique

Mode characteristics of a strongly confined square cavity suspended in air via a pedestal on the substrate are investigated by a three-dimensional finite-difference time-domain technique. The mode wavelengths and mode quality factors (Q factors) are calculated as the functions of the size of the pedestal and the slope angle 0 of the sidewalls of the square slab, respectively For the square slab with side length of 2 mu m, thickness of 0.2 mu m, and refractive index of 3.4, on a square pedestal with refractive index of 3.17, the Q factor of the whispering-gallery (WG)-like mode transverse-electric TE(3.5)o first increases with the side length b of the square pedestal and then quickly decreases as b > 0.4 mu m, but the Q factor of the WG-like mode TE(4.6)o drops down quickly as b > 0.2 mu m, owing to their different symmetries. The results indicate that the pedestal can also result in mode selection in the WG-like modes. In addition, the numerical results show that the Q factors decrease 50% as the slope angle of the sidewalls varies from 90 degrees to 80 degrees. The mode characteristics of WG-like modes in the square cavity with a rectangular pedestal are also discussed. The results show that the nonsquare pedestal largely degrades the WG-like modes. (c) 2006 Optical Society of America

Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes

We provide a detailed expression of the vibrational potential for the lattice dynamics of single-wall carbon nanotubes (SWCNT's) satisfying the requirements of the exact rigid translational as well as rotational symmetries, which is a nontrivial generalization of the valence force model for the planar graphene sheet. With the model, the low-frequency behavior of the dispersion of the acoustic modes as well as the flexure mode can be precisely calculated. Based upon a comprehensive chiral symmetry analysis, the calculated mode frequencies (including all the Raman- and infrared-active modes), velocities of acoustic modes, and the polarization vectors are systematically fitted in terms of the chiral angle and radius, where the restrictions of various symmetry operations of SWCNT's are fulfilled.

Energy spectra of two-electron two-dimensional quantum dots confined by elliptical and bowl-like potentials

The laterally confining potential of quantum dots (QDs) fabricated in semiconductor heterostructures is approximated by an elliptical two-dimensional harmonic-oscillator well or a bowl-like circular well. The energy spectrum of two interacting electrons in these potentials is calculated in the effective-mass approximation as a function of dot size and characteristic frequency of the confining potential by the exact diagonalization method. Energy level crossover is displayed according to the ratio of the characteristic frequencies of the elliptical confinement potential along the y axis and that along the x axis. Investigating the rovibrational spectrum with pair-correlation function and conditional probability distribution, we could see the violation of circular symmetry. However, there are still some symmetries left in the elliptical QDs. When the QDs are confined by a "bowl-like" potential, the removal of the degeneracy in the energy levels of QDs is found. The distribution of energy levels is different for the different heights of the barriers. (C) 2003 American Institute of Physics.

Quantum confinement of phonon modes in GaAs quantum dots

Phonon modes in spherical GaAs quantum dots (QDs) with up to 11,855 atoms (8 nm in size) are calculated by using an empirical microscopic model. The group theory is employed to reduce the computational intensity, which further allows us to investigate the quantum confinement of phonon modes with different symmetries and reveals a phenomenon that phonon modes with different symmetries have different quantum confinement effect. For zinc-blende structure, the modes with the A(1) symmetry has the strongest quantum confinement effect and the T-1 modes the weakest. This could cause a crossover of symmetries of the highest frequency from A(1) to T-2 when the size of QDs decreases. (C) 1999 Elsevier Science Ltd, All rights reserved.

High precision mass measurement and LPT

A Penning trap, which can measure the atomic masses with the highest precision, is one of the most important facilities in nuclear physics research nowadays. The precision mass data play an important role in the studies of nuclear models, mass formulas, nuclear synthesis processes in the nuclear astrophysics, symmetries of the weak interaction and the conserved vector current (CVC) hypothesis. The status of high precision mass measurement around the world, the basic principle of Penning trap and the basic information about the LPT (Lanzhou Penning Trap) are introduced.

Holographic dual of linear dilaton black hole in Einstein-Maxwell-dilaton-axion gravity

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SLL(2, R) x SLR(2, R) Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.

Entropy of Kaluza-Klein black hole from Kerr/CFT correspondence

We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of four-dimensional Kaluza-Klein black hole in Einstein-Maxwell-Dilaton theory. For the extremal Kaluza-Klein black hole, the central charge and temperature of the dual conformal field are calculated following the approach of Guica, Hartman, Song and Strominger. Meanwhile, we show that the microscopic entropy given by the Cardy formula agrees with Bekenstein-Hawking entropy of extremal Kaluza-Klein black hole. For the non-extremal case, by studying the near-region wave equation of a neutral massless scalar field, we investigate the hidden conformal symmetry of Kaluza-Klein black hole, and find the left and right temperatures of the dual conformal field theory. Furthermore, we find that the entropy of non-extremal Kaluza-Klein black hole is reproduced by Cardy formula. (C) 2010 Elsevier B.V. All rights reserved.

A novel approach to isoscaling: The role of the order parameter m = N-f-Z(f)/A(f)

Isoscaling is derived within a recently proposed modified Fisher model where the free energy near the critical point is described by the Landau O(m(6)) theory. In this model m = N-f-Z(f)/A(f) is the order parameter, a consequence of (one of) the symmetries of the nuclear Hamiltonian. Within this framework we show that isoscaling depends mainly on this order parameter through the 'external (conjugate) field' H. The external field is just given by the difference in chemical potentials of the neutrons and protons of the two sources. To distinguish from previously employed isoscaling relationships, this approach is dubbed: m-scaling. We discuss the relationship between this framework and the standard isoscaling formalism and point out some substantial differences in interpretation of experimental results which might result. These should be investigated further both theoretically and experimentally. (C) 2010 Elsevier B.V. All rights reserved.

Recent progress in the studies of endohedral metallofullerenes

This overview presents the recent progress in the area of endohedral metallofullerenes in the past several years. The important results have been summarized as follows: (1) Many metals including Group 3 metals, most of the lanthanide series elements, and Group 2 metals have been encapsulated into a fullerene cage to form mono-, di-, and trimetallofullerenes by using the arc-evaporation technique. (2) Some endohedral metallofullerenes such as Group 3 metals, most of the lanthanide series elements, Group 2 metals, and some of their isomers have been successfully isolated and purified by a two-step or several-step HPLC technique. By using high-temperature and high-pressure extraction with pyridine, Ln@C-80, Ln@C-82, and Ln2@C-80 for most rare-earth metals have been selectively extracted in high yield (about 1% of the saw soot) from fullerenes and other size metallofullerenes. (3) The endohedral nature of metallofullerenes such as Y@C-82, Sc2@C-84, and Sc@C-82 has been finally confirmed by synchrotron X-ray powder diffraction. The symmetries and the structures of metallofullerenes such as Ca@C-82(III), La-2@C-80(I-h), Sc-2@C-84(D-2d), and Sc-2@C-84(C-s) have been confirmed by NMR measurements. (Lb) The information on the electronic structures and properties of endohedral metallofullerenes has been obtained by various spectrometric means Such as EPR, W-vis-MR, XPS, CV. It is generally accepted that three-electron transfer is favorable when M = Y, La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Lu but Sc, Eu, Sm, Yb, Tm, Ca, Sr, Ba prefer to donate two electrons to the fullerene cages. (5) Several chemical reactions of endohedral metallofullerenes have been reported in which reagents are disilacyclopropane, digermacyclopropane, diphenyldiazomethane, and trifluoroacetic acid. (6) Mass spectrometry provided the crucial evidence that led to the discovery of metallofullerenes in 1985 and has always played a key role in their identification and characterization, Ion-mobility measurements of gas-phase ions have obtained the information of structures and the formation mechanism of endohedral metallofullerenes. till Theoretical calculations on the endohedral metallofullerenes have made an important contribution to the studies on the symmetry of the cage, the position of metal atom(s) inside the cage, the number of electronic transfer between metal atom(s) and fullerene cage, etc. (C) 2000 Elsevier Science S.A. All rights reserved.

Structures and vibrational spectra of C-2 and LaC2+ clusters

C-2 and LaC2+ were studied using Hartree-Fock(HF), B3LYP (Becke 3-paremeter-Lee-Yang-Parr) density functional method, second-order Moller-Plesset perturbation (MP2) and coupled cluster singles and doubles with non-iterative triples(CCSD(T)) methods. The basis set employed was LANL1DZ. Geometries, vibrational frequencies and other quantities were reported. The results showed that for C-2, all the methods performed well for low spin state (singlet), while only HF and B3LYP remained so for high spin state (triplet). For LaC2+, four isomers were presented and fully optimized. The results suggested that linear isomers with C-infinity v and D-infinity h symmetries were predicted to be saddle points on the energy surface for all the methods, while for isomers with C-2 upsilon and C-s symmetries, they were local minima except C-2 upsilon at B3LYP level, and were isoenergetic at HF, MP2 and CCSD(T) levels, near isoenergetic at B3LYP level. From the differences between HOMO and LUMO, it is also known that the isomers with C-2 upsilon and C-s symmetries offer the largest values and therefore correspond to the most stable structure. For La-C bond lengths, B3LYP gives the shortest, the order is B3LYP