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Nature has mastered the art of creating complex structures through self-assembly of simpler building blocks. Adapting such a bottom-up view provides a potential route to the fabrication of novel materials. However, this approach suffers from the lack of a sufficiently detailed understanding of the noncovalent forces that hold the self-assembled structures together. Here we demonstrate that nature can indeed guide us, as we explore routes to helicity with achiral building blocks driven by the interplay between two competing length scales for the interactions, as in DNA. By characterizing global minima for clusters, we illustrate several realizations of helical architecture, the simplest one involving ellipsoids of revolution as building blocks. In particular, we show that axially symmetric soft discoids can self-assemble into helical columnar arrangements. Understanding the molecular origin of such spatial organisation has important implications for the rational design of materials with Useful optoelectronic applications. anisotropic interactions | columnar arrangements | helix | self-assembly www.pnas.org./cgi/doi/10.1073/pnas.0906676106

We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn--Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.

Numerical investigations show that the spontaneous break of symmetry in annular incompressible jets occurs in the laminar flow regime and is controlled by both the Reynolds number and the blockage ratio. In the blockage ratio range between 0.50 and 0.89 the transition critical Reynolds number decreases with increasing blockage ratio, according to a defined formula. Transition to asymmetry happens in the steady regime, before the transition to the unsteady flow. Asymmetry is characterized by a preferential flow direction from one side of the jet boundary layer to the diametrically opposite side. The plane of preferential direction passes through the geometry centerline and represents the single plane of flow symmetry. Experiments reported in literature have confirmed the existence of flow asymmetry in an annular jet flow. [DOI: 10.1115/1.3176960] Keywords: annular jets, break of symmetry, laminar flow, CFD

We explore the different local symmetries in colloidal glasses beyond the standard pair correlation analysis. Using our newly developed X-ray cross correlation analysis (XCCA) concept together with brilliant coherent X-ray sources, we have been able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are observed. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction analysis. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron X-ray lasers, an accurate and systematic experimental characterization of the structure of the liquid and glass states. coherent X-ray diffraction | higher-order correlations | structure

Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low-temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered-cubic lattice and has a packing fraction of [pi]/(3[square root of 2]) ~ 0.7405. Much more recently, an unusually high-density packing of [approximately equal to] 0.770732 was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here, we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of high-density packing whose order is characterized by a broken symmetry arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of [pi]/4. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio c of the base radii of the truncated cones with a transition at [c.sup.*] = [square root of 2] - 1. biaxial order | packing | truncated cones

We discuss under what conditions multiple-parameter asymmetric linear dynamical systems can be transformed into equivalent symmetric systems by nonsingular linear transformations. So far, in structural dynamics literature this problem has been addressed in the context of the original work by Taussky. Taussky's approach of symmetrization was based on similarity transformation. In this paper an approach is proposed to transform asymmetric systems into symmetric systems by equivalence transformation. We call Taussky's approach of symmetrization by similarity transformation 'first kind' and proposed approach by equivalence transformation 'second kind.' Since equivalence transformations are most general nonsingular linear transformations, conditions of symmetrizability obtained here are more 'liberal' than the first kind and numerical calculations also become more straightforward. Several examples are provided to illustrate the new approach. [S0021-8936(00)00504-3]

Reasoning from two basic principles of molecular physics, [Mathematical Expression Omitted] invariance of electromagnetic interaction and the second law of thermodynamics, one would conclude that mirror symmetry is retained in the world of chiral molecules. This inference is fully consistent with what is observed in inorganic nature. However, in the bioorganic world, the reverse is true. Mirror symmetry there is definitely broken. Is it possible to account for this phenomenon without going beyond conventional concepts of the kinetics of enantioselective processes? This study is an attempt to survey all existing hypotheses concerning this phenomenon.

The application of multipole and symmetry connection principles to numerous point groups and multipoles is not available in most chemical literature despite the importance of this application to teaching intermolecular interactions. Group theoretical derivations for the expansion of the electrostatic energy term in multipole/multipole interactions are presented as is a table of the 48 most common point groups and their explicit derivations.

Convective effects determine the pattern of electrodeposition of metals from solutions of their salt. Convective effects affect the electrodeposition of iron from FeSo4 solution and lead to the formation of a mesh-like pattern, as observed by interference contrast microscopy and transmission optical dark field microscopy. A reduction in pH reduces convection and shifts to dense branching pattern of deposition.

Mechanical motions and disturbances of growing branches of metal ions in solution modify morphology patterns between fractal and rectilinear states. A study of electrochemical deposition of ramified deposits reveals that high growth speeds break the symmetry of fanning in the growing branches and cause differential growth patterns. The experiment parameters also determine the final pattern detected.

The charge density wave behavior of ultra-thin films of lead adsorbed on germanium is accompanied by metal-nonmetal transition and periodic lattice distortion. The structural symmetry of the system is broken and the molecular orbits degenerate so that an electron can occupy a lower energy level. The lead-germanium system is non-metallic in the low temperature, distorted phase due to the band gap. This behavior can be used to produce specific electronic characteristics by tailoring interface and surface properties.

Spontaneous symmetry-breaking in magnets and soap films is discussed. Ferromagnetism is the most common type of spontaneous symmetry breaking and is related to the unpaired spin on each atom of iron. Chiral symmetry as demonstrated by the optical activity of sugars is another example of spontaneous symmetry breaking at the molecular level which is expressed in the macroscopic level. Understanding spontaneous symmetry breaking could help in engineering molecules to express useful patterns.

Most engineering material behaviors can be described by using nonassociated plasticity models, but their use leads to the formation of unsymmetric matrices that have, to date, been resolved by nonsymmetric solvers, the initial stiffness method, and, more recently, some symmetrization techniques. Some of these methods have proved to be inefficient due to large core storage requirements, excessive iteration, and slow rate of convergence; or the existence of regions of numerical instability within the mapping process. Some robust techniques are outlined in this paper that are capable of providing solutions of acceptable accuracy for nonassociated plasticity problems, by adapting them for banded, symmetric solvers and by returning CPU times comparable to the best available solution techniques. Numerical solutions to problems in both soil and nongranular plasticity are provided to illustrate the capability of the proposed techniques, and the problem of numerical instability inherent in a previous symmetrization technique is addressed.

Exact symmetry fits into an outmoded mechanical model of molecular structure and may be replaced by a newly developed system of continuous symmetry measures. Continuous symmetry is a measure of degrees of deviation from a rotational or mirror symmetry. In two-dimensional cases, the measure is easily determined by comparison of a structure with its images in a hypothetical symmetrized set representing the nearest object with the desired symmetry. The situation is more complex in three-space. These measures should be of use in parametrizing property surfaces in anisotropic non-equilibrium geometries.

The usual method of predicting molecular chirality is through the inspection of a symmetry element, but achirality does not require a symmetry plane. A molecule is achiral if the process of transforming from a chemical conformation to a mirror image through chemical-bond rotation is easy to accomplish. The process of finding a chemical conformation with a rotating plane of symmetry then becomes simple.