Symmetry Aspects Research Articles

Aspects of chiral symmetry and the lattice

This article is a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, the author discusses how anomalies complicate lattice formulations. Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for lattice models and elucidating the role of the CP-violating parameter \ensuremath{\Theta}. One particularly elegant scheme for exploring this physics on the lattice is presented in some detail. This uses an auxiliary extra space-time dimension, with the physical world being a four-dimensional interface.

Chirality and symmetry aspects of spheroarenes, including fullerenes.

The design of the smallest spheroarenes (C(N) molecules based on trivalent polyhedral framework, a class which subsumes fullerenes) of any point-group symmetry is presented. The role of Curie's principle is discussed. Some molecules whose carbon backbone is a nonplanar graph are described.

Light-front aspects of chiral symmetry

Spontaneous chiral symmetry breaking and axial anomaly are studied in the light-front formulation. The existence of multiple vacua and a Nambu-Goldstone boson, both related to dynamical fermion zero modes, are demonstrated within a simple sigma model with fermions. The Weyl gauge formulation and a consistent gauge invariant point-splitting regularization, which includes the light front time, are crucial for obtaining the anomaly in the massive Schwinger model and QED(3+1).

Optical Second-Harmonic Generation in Benzophenone

Introduction Versatile and efficient sources of blue light are of fundamental importance for various applications including optical data storage [1,2], ophthalmologic or other medical techniques [3], and laser displays [4 to 6]. In spite of the rapid development of blue laser diodes [7,8] and concurrent physical principles like optical upconversion[9], the optical second-harmonic generation [10] (SHG) still is one of the most important methods to achieve intense coherent blue light with a good optical beam quality [11]. From symmetry aspects, SHG is only possible in crystals belonging to one of the 20 point groups which lack a center of symmetry [12]. Furthermore, to meet phase matching aspects in homogeneous crystals, refractive indices for the fundamental and the generated harmonic wavelength must be of identical size [13,14], optical birefringence is necessary. Here we discuss the properties of benzophenone (C 13 H 10 O), an organic crystal, which excellently meets the described conditions. Crystal Properties Crystals of benzophenone can be grown from the melt (melting point approximately 48°C) [15]. The crystal structure is orthorhombic with point symmetry 222. This forces the material to be optically biaxial with the axes of the indicatrix fixed to the three mutually perpendicular symmetry axes of the crystal. Theoretical studies revealed - due to the conjugated bonds - a good second order nonlinear optical polarizability [16]. Optical Absorption For optical applications in general - and especially for SHG - the material considered must be transparent in the wavelength region of interest. Measurements of the optical absorption in benzophenone show a region of excellent transparency spanning from 390 to 1700 nm. Depending on light polarization - parallel or perpendicular to the crystallographic c-axis - two typical spectra are found. The experimental results are sketched in Fig. 1.

Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion

We consider some aspects of conformal symmetry in a metric-scalar-torsion system. It is shown that, for some special choice of the action, torsion acts as a compensating field and the full theory is conformally equivalent to General Relativity on classical level. Due to the introduction of torsion, this equivalence can be provided for the positively-defined gravitational and scalar actions. One-loop divergences arising from the scalar loop are calculated and both the consequent anomaly and the anomaly-induced effective action are derived.

Validating Cluster Analysis: Consistent Replication and Symmetry

Two simulation studies evaluated a cross-validation approach for cluster analyses (CA). Study 1 examined the extent to which the magnitude of replication and two aspects of replication, consistency and symmetry indicate recovery of true clusters for ten CA algorithms. Cluster size, number of clusters, covariance structure, number of variables, sample size, and error perturbation were systematically varied. Replication indices significantly predicted recovery. Study 2 evaluated replication as an indicator of the number of true clusters within a sample. Although on the average replication indices peak in the region of the true number of clusters, choosing the number of clusters by maximum replication results in a negatively biased estimate. A proposed "scree test" attenuates this bias, however, and improves accuracy.

Fast exact minimization of BDD's

We present a new exact algorithm for finding the optimal variable ordering for reduced ordered binary decision diagrams (BDD's). The algorithm makes use of a lower bound technique known from very large scale integration design. Up to now this technique has been used only for theoretical considerations and it is adapted here for this purpose. Furthermore, the algorithm supports symmetry aspects and uses a hashing based data structure. Experimental results are given to demonstrate the efficiency of our approach. We succeeded in minimizing several functions, including adders with up to 64 variables, for which all other previously presented approaches fail.

Symmetry aspects of the existence of high-velocity SAW in layered composites

An analysis is performed of the equations governing the existence of surface acoustic waves (SAW) propagating on the plated surface of a solid with the velocity exceeding the velocity of two quasi-transverse bulk waves in the substrate. If the direction of propagation assumes particular orientations in reference to the elements of crystallographic symmetry of the substrate and layer, then there are only three relations to be fulfilled for high-velocity SAW to arise. These relations determine the SAW velocity, the layer thickness/wavelength ratio, and the orientation angle of the sagittal plane.

Combinatorics of giant hexagonal bilayer hemoglobins

The paper discusses combinatorial and probabilistic models allowing to characterize various aspects of spacial symmetry and structural heterogeneity of the giant hexagonal bilayer hemoglobins (HBL Hb). Linker–dodecamer configurations of HBL are described for two and four linker types (occurring in the two most studied HBL Hb of Arenicola and Lumbricus, respectively), and the most probable configurations are found. It is shown that, for HBL with marked dodecamers, the number of `normal-marked' pairs of dodecamers in homological position follows a binomial distribution. The group of symmetries of the dodecamer substructure of HBL is identified with the dihedral group D 6. Under natural symmetry assumptions, the total dipole moment of the dodecamer substructure of HBL is shown to be zero. Biological implications of the mathematical findings are discussed.

Teaching maths through theme-based resources: Pedagogic style, `theme' and `maths' in lessons

The design and use of curriculum resources which relate mathematics to our social and cultural reality has been valued as encouraging meaningful learning of the subject. But, how teachers apply such resources in their pedagogic practice remains a question worth investigating. This paper explores two maths teachers' ways of employing theme-based resources in their lessons. Based on the theme of art (i.e. Roman Mosaics and decorative patterns that can exemplify aspects of symmetry), a set of activities was devised and offered to teachers for use. Teachers' ways of implementing these resources were charted through a long-term ethnographic study. Classroom observation, transcripts of classroom talk and interviewing were the main tools used to seek teachers' views and to characterise teaching. Analysis of data provides a detailed look at how teachers of diverse pedagogic orientations use thematic contexts in their teaching of mathematics. Specifically, the extent to which teachers' pedagogic styles influence their ways of placing `theme' and `maths' in lessons is being explored and discussed.

Symmetry in Plants: Introduction

Symmetry pervades nature. “Ultimately, at the centre of na-ture, we find mathematical symmetries” (Heisenberg 1966, p.38).Ineverydaylifesymmetriesaremostobviousinorganisms.If we look more closely, symmetries not only are present atthe surface of organisms but pervade organisms at many levels(Garcia-Bellido 1996).Today, symmetry is of interest to a broader diversity of bi-ologists than ever before. From molecular geneticists (e.g.,Coen 1996; Sessions and Yanofsky 1999) to ecologists (e.g.,Karban and Thaler 1999), the symmetry of form in plants isunder intensive study.The expression of vegetative and reproductive shoot sym-metries among plants is extremely diverse. Morphologists rec-ognize two basic categories of shoot symmetry: rotational ortransectional symmetry and longitudinal or translational sym-metry. The first is the symmetry of shoots when viewed incross section, whereas the second encompasses variation alongthe length of the shoot. Within each category, the particulartype of symmetry can be determined by numerous attributes,including organ size, shape, and placement. Although mor-phologists have long studied symmetry, other aspects of sym-metry are largely unexplored.We have assembled a collection of articles on shoot sym-metry with the goal of exploring fundamental issues of thedevelopment, function, and evolution of shoot symmetry.Shoot symmetry is expressed during development. Can theanalysis of development discover basic patterns of change thatresult in diverse symmetries? How does symmetry change dur-ing development? What do deviations from symmetry indicateabout the stability of developmental processes and the con-dition of the organism as a whole? Symmetry patterns areextremely diverse, yet similar patterns of symmetry haveevolved independently in unrelated taxa. Such patterns of ev-olutionary convergence often indicate similar selection pres-sures (Wake 1991). What is the functional significance of dif-ferent types of symmetry? Are particular symmetries adaptive?What are the patterns of evolutionary diversification ofsymmetry?We bring together researchers who approach the study ofsymmetry from widely divergent points of view and who con-duct research inspired by very different kinds of questions.Their articles address symmetry from the following perspec-tives: the symmetry of form, symmetry of development in-cluding developmental asymmetry as noise in a regular sym-metrical pattern, the function of symmetry, and themaintenance and change of symmetry during developmentandevolution. Each article explores developmental, functional,and/or evolutionary aspects of symmetry. Because most of thearticles are concerned with more than one aspect of symmetry,we have organized them according to the type of symmetryrather than by the conceptual issues they address.The first series of articles addresses transectional symmetry.Four papers deal with different aspects of floral transectionalsymmetry, including developmental constraints, functionalconstraints, and the perception of symmetry by pollinators.Symmetry in flowers is favored over irregularity because ofdevelopmental economy, mechanical pollination efficacy, andvisual attractiveness for pollinators. Peter Endress gives anoverview of the diversity of symmetry in flower form and de-velopment within the context of function and evolution, in-cluding new examples and perspectives on enantiomorphy.Shirley Tucker reviews the lability of early developmentalsym-metry patterns of flowers in flowering plants. She shows thatsymmetry patterns may differ among closely related plantgroups in early development, although they are similar at ma-turity. Martin Giurfa, Amots Dafni, and Paul Neal review thefunction of floral symmetry and its role in plant-pollinatorsystems. They explore the question of whether symmetry (vs.asymmetry) can be perceived by bees and whether symmetryis used by bees as a signal. Miriam Lehrer looks at flowersymmetryfromthepointofviewofthepollinators.Shereviewsthe kinds of spatial signals perceived by bees in light of spatialsignals that flowers display and the importance of display dis-tance and display angle. The contributions by Nancy Denglerand Rolf Rutishauser each review a special pattern of shoottransectionalsymmetrythathasevolvedseveraltimesandfromdifferent precursor (ancestral)patternsthroughoutlandplants:shoots with anisophylly and shoots with polymerous whorls.Both authors survey various aspects of development,structure,and function of these patterns, the first with additional em-phasis on physiology and the second on systematics.A second series of articles discusses the longitudinal sym-metry of vegetative shoots. Cynthia Jones provides an analysisof phase change and heteroblasty. These two phenomena typ-ically are conflated in the literature, but Jones argues that theyare separate biological phenomena, and she provides an anal-ysis of how they might be defined and circumscribed. Thecontribution by Alice Winn discusses the possible functionalrole of heterophylly. A review of the literature and her ownresearch shows that both phenotypic plasticity and pro-grammed ontogenetic changes contribute to the expression ofheterophylly. She demonstrates that heterophylly enhancesleafphysiological function in one species, but there is no relationbetween leaf traits and fitness in another species of annualplant. Pamela Diggle explores the relationship between shootheteroblasty and evolutionary changes in flowering time. Dueto the heteroblastic nature of virtually all plants, changes inflowering phenology invariably will result in changes in veg-etative morphology.

Chirality and general aspects of symmetry.

The phenomenon of chirality is described in terms of symmetry and via symmetry operators.

Deposition and drive symmetry for light ion ICF targets

Light ion beam ICF is a concept in which intense beams of low atomic number ions would be used to drive ICF targets to ignition and gain. Three dimensional analytic approximations indicate that at least twelve beams would be required to drive an indirect drive target with adequate symmetry. Here, results from two dimensional numerical simulations are presented describing the ion deposition and drive symmetry aspects of such a target for which the ion beams are approximated as ring sources. For adequate symmetry in the two dimensional calculations, the simulations required six ring sources and two pole sources during the low power `foot' pulse and four ring sources during the main ion beam drive pulse. If each ring represents five individual beams, this corresponds to 32 beams in the foot pulse and 20 beams in the main pulse. The corresponding two dimensional integrated LASNEX calculation, simulating the target from ion beam input to ignition and burn in the same code run, produced 591 MJ of thermonuclear yield with lithium ion beam sources containing a total input energy of 16 MJ.

Apomorphy Distribution Is an Important Aspect of Cladogram Symmetry

Apomorphy Distribution Is an Important Aspect of Cladogram Symmetry

Particle-hole excitations in the interacting boson model (IV). The U(5)-SU(3) coupling

In the extended interacting boson model (EIBM) both particle- and hole-like bosons are incorporated to encompass multi-particle-multi-hole excitations at and near to closed shells. We apply the group theoretical concepts of the EIBM to the particular case of two coexisting systems in the same nucleus exhibiting a U(5) (for the regular configurations) and an SU(3) symmetry (for the intruder configurations). Besides the description of “global” symmetry aspects in terms of I-spin, also the very specific local mixing effects characteristic for the U(5)-SU(3) symmetry coupling are studi d. The model is applied to the Po isotopes and a comparison with a more realistic calculation is made.

New Cosmological Solutions from Soliton Transform Technique

In this talk, a brief introduction to string cosmology is given in the beginning. We recall duality symmetries and the main ingredients of pre-big bang scenario in the context of string theory. One of the interesting aspects of stringy T-duality symmetry is the possibility of generating new cosmological solution starting from a known solution of the string effective action. In the later part of the talk, we apply the soliton transformation technique, in the string cosmological context, to obtain new background solutions. These backgrounds satisfy the equations of motion by construction.

Superstructure formation of large organic adsorbates on a metal surface: A systematic approach using oligothiophenes on Ag(111)

A series of ‘‘end-capped’’ oligothiophenes ECnT with different chain lengths n (n53 ‐ 6) were vapor deposited onto the Ag~111! surface. The adsorption and structural ordering was investigated by thermal desorption spectroscopy, low-energy electron diffraction, and scanning tunneling microscopy. For all molecules we observe highly ordered monolayers with flat-lying molecules and long-range ordered domains of several hundred A diameter. For the two smaller oligomers~EC3T and EC4T!, two phases—a commensurate ~relaxed! and an incommensurate ~compressed!—are found, whereas the two longer molecules ~EC5T and EC6T! form only incommensurate phases. The six unit cells exhibit significantly different symmetries, containing 1, 2, or 4 molecules. The formation of the geometric structures is discussed under the aspect of molecular size, molecular symmetry, and interplay of the molecule-substrate and molecule-molecule interactions. The last aspect was also investigated by concomitant force-field calculations. @S0163-1829~98!02143-2#

Properties of a new weak ferroelectric-cyclohexane-1,1′-diacetic acid

Data on the calorimetric, dielectric and infrared properties of a molecular crystal cyclohexane-1,1′-diacetic acid around its 397 K ferroelectric phase transition are presented and discussed. The DSC experiments confirm the first order character of the phase transition and the dielectric measurements reveal a relaxation soft mode in an unusually low frequency region 10 3–10 4 Hz. Detailed analysis of the possible nature of the pseudoproper ferroelectric phase transition is based on the symmetry aspects.

Multicolour models of natural embedding for SU(2≥m≥4)× S 10 ↓ D 5 NMR spin symmetry: Determinacy of nuclear spin weights for (1,12)-car -11 B-boranes

The inherent (in)determinacy implicit in the SU(m≥3)×Sn↓G natural embedding aspects of (NMR) spin symmetry of clusters is investigated, as part of a multicolour modelling scheme, where the SU2-branching level meets the initial n(Sn)=/G/ condition. We focus on correlative mappings derived from [λ]SA (self-associate) irreps for natural group embeddings and compare these with certain Yamanouchi-Gel'fand chain properties of S10 Mathematical decompositions of Mλ simple Sn-modules with (2≥p≥4)-branchings of λ⊵,λSA (for λ⊢N partitions of n) provide the initial insight into the monocluster spin (NP) physics of [2H]10, [11B]10 (S10↓D5), as aspects of (1,12)-(HC)2(11B)10 or (HC)2(211B10 carborane cage isotopomers. The questions raised are significant for their impact on CNP nuclear spin weighting of ro-vibrational spectra. The methods used are those of combinatorics-via-group actions, as physical Sn-encodings applied to nuclear spin algebras.

Symmetry aspects of nonrigid molecules and transition structures in chemical reactions

Symmetry aspects of nonrigid molecules and transition structures in chemical reactions