Symmetry Relationships Research Articles

Symmetry relations of magnetic twin laws.

Symmetry relationships between two simultaneously observed domain states (domain pair) are used to determine physical properties that can distinguish between the observed domains. Here the tabulation of these symmetry relationships is extended from non-magnetic cases to magnetic cases, in terms of magnetic point groups, i.e. all possible magnetic symmetry groups and magnetic twinning groups of domain pairs are determined and tabulated.

Symmetry and structural relationships among ABW-type materials

Abstract The symmetry relationships among zeolite-type ABW compounds are described in terms of the reductions of symmetry from the highest possible topological symmetry in space group Imam to eight possible subgroups. This family of compounds, also known as Icmm-type compounds, covers a wide range of chemical compositions. The distortion modes inducing the lowering of symmetry are described based on rotation and ordering processes. Atomic site relationships with their evolution from the aristotype are given for the recently described monoclinic P1121/n structures with an ABW-type framework.

Z' = 4 structure without obvious pseudosymmetry: implications for the formation of solid-state compounds.

Crystals of 4-chloro-2'-biphenylol grown at 263 K and studied at both 293 and 142 K are loosely packed and contain OH.O bonded tetramers composed of four crystallographically independent molecules (Z' = 4). Approximate symmetry relationships between independent molecules are apparent in many, perhaps even most, structures with Z' > 1, but are not obvious in this structure. The inefficient crystal packing, the surprisingly large value of Z' and the absence of pseudosymmetry reflect the difficulty of finding a dense molecular arrangement that also allows for hydrogen-bond formation. Impediments to good packing are the steric congestion around the ortho hydroxyl groups and the difficulty in filling space with significantly twisted biphenyl fragments. The packing arrangement adopted is strongly reminiscent of the structure type found for eight simple 4,4'-biphenyl derivatives, but one of the four independent 4-chloro-2'-biphenylol molecules has an orientation that is significantly different from the orientations of the other three and that does not fit the 4,4'-XPhPhY pattern. It is suggested that molecules that crystallize with Z' > 1 are good candidates for solid-state compound formation.

Graph-set and packing analysis of hydrogen-bonded networks in polyamide structures in the Cambridge Structural Database.

The hydrogen-bond networks and crystal packing of 81 unique secondary di- and polyamides in the Cambridge Structural Database are investigated. Graph-set analysis, as implemented in the RPluto program, is used to classify network motifs. These have been rationalized in terms of the relative dispositions of the amide groups. Peptide and retropeptides exhibit significant conformational flexibility, which permits alternative hydrogen-bonding patterns. In peptides, dihedral angles of -psi approximately varphi approximately 105 degrees allow an antiparallel ladder arrangement, containing rings of either the same or alternating sizes. For retropeptides, and diamides with an odd number of CH(2) spacers, this conformation leads to a parallel ladder with rings of equal size. If varphi approaches -60 degrees and psi 180 degrees, ladders adopt a helical twist, and if the conformation is distorted further, a three-dimensional network is usually adopted. Diamides with aromatic or an even number of CH(2) spacers generally form either antiparallel ladders or sheets, although some exhibit both polymorphs. Symmetry relationships within and between hydrogen-bonded chains, ladders and sheets in the crystal packing have also been analysed. Polyamides form considerably more complex networks, although many of the structural motifs present in the diamides occur as components of these networks.

Symmetry and structure in P-glycoprotein and ABC transporters what goes around comes around.

The ABC superfamily of membrane transporters is one of the largest classes of proteins across all species and one of the most intensely researched. ABC proteins are involved in the trafficking of a diverse variety of biological molecules across cell membranes, with some members implicated in medical syndromes such as cystic fibrosis and multidrug resistance to anti-cancer drugs. In the absence of X-ray crystallographic data, structural information has come from spectroscopy, electron microscopy, secondary structure prediction algorithms and residue substitution, epitope labelling and cysteine cross-linking studies. These have generally supported a model for the topology of the transmembrane domains of ABC transporters in which a single aqueous pore is formed by a toroidal ring of 12 alpha helices, deployed in two arcs of six helices each. Although this so-called 6 + 6 helix model can be arranged in either mirror or rotational symmetry configurations, experimental data supports the former. In this review, we put forward arguments against both configurations of this 6 + 6 helix model, based on what is known generally about symmetry relationships in proteins. We relate these arguments to P-glycoprotein, in particular, and discuss alternative models for the structure of ABC transporters in the light of the most recent research.

Analytical expressions for the radiation emergent from a scattering medium exposed to a polarized laser beam

Analytical expressions for the spatial variation of the radiation emergent from a multiple-scattering medium exposed to a polarized laser beam are developed. The medium is finite in the vertical direction and infinite in the radial direction. The three-dimensional radiative transfer is described by the vector transport equation. The intensity vector is comprised of the four Stokes parameters, and the scattering is described by a general phase matrix for randomly oriented particles with a plane of symmetry. The radiation incident on the upper surface is cylindrically symmetric, perpendicularly directed, collimated, and polarized, e.g. a Gaussian laser beam. Expressions for the reflection and transmission matrices are presented for this specific loading and the case of normally emergent radiation. Symmetry relationships and matrix rotations are applied to obtain special forms of the normal reflection and transmission matrices. This procedure allows part of the inverse transform to be performed analytically and the angular variation of the reflection and transmission matrices to be found explicitly. The emergent intensity for an unpolarized or circularly polarized beam depends on only the radius; the intensity distribution is two dimensional. For a linearly polarized laser beam, the intensity exhibits three-dimensional effects; the spatial variation of the backscattered and transmitted intensities depends on both the radius and azimuthal angle. Thus, the polarization of the incident radiation can cause the intensity distribution to be either two- or three-dimensional.

Crack propagation: Dynamic stochasticity and scaling

The results of theoretical and experimental investigations provide explanation of the mechanism of stochastic branching during crack propagation in a solid, relating this phenomenon to changes in the fundamental symmetry relationships in a nonlinear system representing the solid with defects. The character of the stochastic behavior of quasibrittle materials is determined by nonlinear dynamics of the ensemble of microscopic defects under the conditions of kinetic transitions. The transition from dispersed to macroscopic fracture is accompanied by the appearance of multiple fracture zones in the regime of explosion-like instability development over a discrete spectrum of spatial scales.

Detecting symmetric patterns in EEG data: a new method of analysis.

Theoretical models of higher cognitive function predict that cortical activity will exhibit families of spatial-temporal patterns of activity whose individual members are related to each other by specific symmetry transformations. In the trion model, it is suggested that these inherent symmetries play a vital role in how we think and reason. We have developed a method of analysis (SYMMETRIC analysis), which detects families of patterns in EEG data, and characterizes the symmetry relationships between members of those pattern families. Using this analysis, significant symmetry families have been found in EEG and single unit spike train data. If symmetry is a crucial aspect of brain function, it is possible that different pathologies are associated with specific types of symmetry relationships in brain activity that could be detected in EEG data by a SYMMETRIC analysis.

Envelope skeletonization as a means to determine monomer masks and non-crystallographic symmetry relationships: application in the solution of the structure of fibrinogen fragment D.

An algorithm is described which utilizes the solvent mask generated by the solvent-flattening technique to calculate a monomer molecular envelope. In the case where non-crystallographic symmetry (NCS) is present in the crystal and self-rotation angles are known from a self-rotation function, the resultant monomer envelopes can be used to search for the translation component of the NCS element by a three-dimensional search in real space. In the absence of self-rotation angles, the monomer envelope may be used to derive the NCS operators by reciprocal-space techniques. Thus, an automatic procedure for averaging directly from the solvent-flattening stage can be implemented. The procedure was instrumental in the structure solution of fibrinogen fragment D, which is presented as an example.

Electronic Structure Measurements of Colossal Magnetoresistive Manganese-Oxides: Polaronic Effects on the Band Structure

We have used high energy-resolution angle-resolved photoemission spectroscopy(ARPES) to map the k-dependent electronic structure of single-crystallinesamples of the manganese-based perovskites as a function of doping level, temperature,and layer number. The measured near-Fermi energy states display E vs. kand symmetry relationships which agree relatively well with the LSDA band theoryprediction through much of the Brillouin zone, and the locus of lowest energy excitations matches the predicted large Fermi surface quite well. However, thespectralfeatures are too broad to be well described as Fermi-Liquid likequasiparticles, and they are strongly suppressed from the Fermi energy, e.g., there is apseudogap in the excitation spectrum. We discuss the spectral properties interms of strong coupling to a local effect such as a lattice distortion.

K-Dependent Electronic Structure, a Large “Ghost” Fermi Surface, and a Pseudogap in a Layered Magnetoresistive Oxide

The $k$-dependent electronic structure of the low temperature ferromagnetic state of ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ was measured using angle-resolved photoemission spectroscopy and calculated using the local spin density approximation (LSDA). The measured near-Fermi energy states display $E$ vs $k$ and symmetry relationships which agree relatively well with the LSDA prediction through much of the Brillouin zone, and the locus of lowest energy excitations matches the predicted large Fermi surface quite well. However, the spectral features are too broad to be well described as Fermi-liquid-like quasiparticles, and they are strongly suppressed from the Fermi energy, i.e., there is a pseudogap in the excitation spectrum. We discuss the spectral properties in terms of strong coupling to a local effect such as a lattice distortion.

Modeling crystallographic texture evolution with finite elements over neo-Eulerian orientation spaces

A novel methodology is presented for the modeling of crystallographic texture based on the application of finite elements to represent and compute the orientation distribution function (ODF) over explicit discretizations of orientation space. Various orientation spaces are examined for this purpose. The neo-Eulerian axis angle spaces of Frank are preferred over the conventional Euler angle spaces for their superior properties. Properties of the neo-Eulerian spaces required by the modeling are derived. These include the reduction of the spaces under crystal symmetries to fundamental regions, the consequent boundary symmetry relationships, and the various Riemannian metrical properties of the spaces. The structure of crystal flow generated under the uniaxial extension of FCC crystals is examined over the cubic fundamental region of Rodrigues' space. Stabilized finite element schemes for the ODF conservation equation, developed previously for the texturing of planar polycrystals, are extended to the three-dimensional texturing considered. Properties of the schemes are illustrated by application to the texturing of FCC polycrystals over Rodrigues' space.

Strong dependence of multichannel ballistic transport on the geometric symmetry

Ballistic electron transport in Aharonov–Bohm-type ring structures is investigated where the single-channel problem is nontrivially extended to the multichannel one in which the important interchannel scattering effect is considered. It is found that theS-matrix of a ring structure should reflect the geometric symmetry if the interchannel scattering effect is properly accounted for and that the symmetry relationships of theS-matrix plays a crucial role in the conductance oscillation behavior in ballistic two-dimensional rings. The magnetostatic as well as the electrostatic Aharonov–Bohm effects are studied for two ring structures of different symmetry.

Three-dimensional radiative transfer with polarization in a multiple scattering medium exposed to spatially varying radiation

The present investigation of three-dimensional radiative transfer accounts for polarization and multiple scattering by using the vector transport equation. The intensity vector is comprised of the four Stokes parameters, which are functions of three coordinates describing position and two angles specifying direction. Scattering is characterized by a general phase matrix for randomly oriented particles with a plane of symmetry. The medium is finite in the z-direction and infinite in the x- and y-directions. The incident radiation is polarized and spatially varying on the upper boundary. The vector transport equation is converted, using a double Fourier transform, to an ordinary integro-differential equation with a complex coefficient. The problem of collimated radiation incident on the upper boundary of a cylindrical medium is shown to be of fundamental importance. The analysis is greatly simplified by expressing the transformed intensity vector in a form that depends on only one transform variable. Using superposition, a linear Fredholm integral equation of the second kind is developed for the 4 × 4 generalized source matrix. The bidirectional reflectance and transmittance of a scalar analysis are replaced by 4 × 4 reflection and transmission matrices. The emergent radiation can be determined from these matrices for incident radiation of any polarization. Symmetry relationships are developed using successive orders of scattering and symmetry properties of the phase matrix.

Preliminary study on stimulus equivalence in beluga (Delphinapterus leucas)

Dolphins are thought to possess high cognitive and intellectual skills. The present study investigated the early or spontaneous establishment of the stimulus equivalence in a beluga whale in order to gain insight into the cognitive process in dolphin. First, the subject participated in an object-naming task using conditional discriminations within a matching - to - sample paradigm. The beluga whale could name three objects with alphabet like letters. Next, the subject was trained in A → B and B → C matching and tested with B → A (symmetry), A → C (transitivity) and C → A (equivalence) relations in probe trials. The performance was low in both symmetry and equivalence relationships but high in transitivity relationships. This provides the first empirical evidences for a beluga whale to develop untrained relationships based on trained relationships of stimulus sets.

Accelerating the discrete ordinates method for the solution of the radiative transfer equation for planetary atmospheres

The discrete ordinates method is widely used in one-dimensional radiative transfer problems. The equation of transfer contains an integral over all directions to represent the multiple scattering of radiation. In the discrete ordinates method one of the integrals can be performed after a Fourier expansion is made for the scattering function and the radiance. The remaining integral is replaced with a Gauss quadrature sum and a system of ordinary differential equations is found. The system of ODEs is linear, and can be solved together with the boundary conditions by standard matrix methods. It is well known that symmetry relationships allow the order of the matrices that occur in the eigenproblem to be reduced by a factor of two. However the resulting gain in efficiency is strongly compromised by the size of the remaining tasks of calculating the particular solution, and determining the unknown coefficients from the boundary conditions. In this paper we show that further increases in computational efficiency are available. First we find that the order of the matrix inversion that arises in the particular solution can be reduced. We then show that the equations that determine the coefficients from the boundary conditions can be reduced in order in the case of a one-layer system with a nonLambertian reflecting surface.

Symmetry relationships in the homeotypical aluminium-rich structures with pentagonal channels

Symmetry relationships in the homeotypical aluminium-rich structures with pentagonal channels

Non-magnetic twin laws

Twin laws are groups that express the symmetry relationships between two simultaneously observed domain states (domain pair) and are used to determine physical properties that can distinguish between the observed domains. A tabulation is presented of all possible non-magnetic twin laws, that is, all possible symmetry groups and twinning groups of the domain pair. Additional information is provided related to determining twin laws. This includes the coset and double-coset decomposition of point groups, the indexing and point-group symmetry of domain states, permutations of domain states, and a classification of domain states.

Molecular packing analysis. Part 3. The prediction of m-nitroaniline crystal structure

Molecular packing analysis of m-nitroaniline was carried out in order to study whether it is possible to predict the crystal structure of systems that include hydrogen bonds. Off-ridge eigenvector minimization with annealing (OREMWA) was carried out with Biosym's potential parameters and potential-derived charges obtained from an ab initio Hartree-Fock calculation using the 6-31++G ∗∗ basis set. Two types of initial structure were prepared for the OREMWA calculations (ten structures were created for each type of initial structure). The first-type initial structures were created by deforming the observed crystal structure up to 1 Å in the unit cell lengths and molecular translations, and up to 10 ° in the unit cell angles and molecular rotations. The second-type initial structures were created by four molecules satisfying space symmetry relationships of the observed space group Pbc2 1 in a 12 A ̊ × 12 A ̊ × 12 A ̊ cubic unit cell. In the second-type initial structures, the orientation of a reference molecule was determined randomly. Molecular translation variables of three molecules, molecular rotation valuables of all four molecules, and six unit cell parameters were varied in the OREMWA calculations starting from the first-type initial structures. Molecular translation variables and molecular rotation variables of a reference molecule, and cell lengths only, were varied in the OREMWA calculations starting from the second-type initial structures in order to retain the observed space group symmetry, because the Pbc2 1 space group is orthorhombic with 90 ° cell angles. This space group is also polar in the c-axis direction, so that one molecular origin in this direction is fixed. The observed crystal structure of m-nitroaniline was reproduced as the most stable crystal structure starting from both types of initial structure.

Symmetry of a Vertebrate Muscle Basketweave Z-Band

The Z-band in vertebrate striated muscle links actin filaments of opposite polarity in adjacent sarcomeres to form a regular structure based on a tetragonal lattice. In transverse sections there are two commonly observed appearances of the Z-band seen in different muscles, namely, the small-square lattice and the basketweave forms. A clear example of the latter occurs in the fin muscle of the flatfish plaice and its symmetry is described here. Improved methods over previous work include fast freezing/freeze-substitution and lattice straightening of the scanned images. It is demonstrated here that when a longitudinal section is tilted in the electron microscope about the myofibril axis, the 10 and 01 projections are mirror images of each other about the centre of the Z-hand. By examining the symmetry relationships between these views and a longitudinal 11 projection and a transverse view, it is concluded that the symmetry is best described by the two-sided plane group c12. The twofold axis lies in the central plane of the Z-band along the diagonal of the primitive lattice and runs normal to the actin filaments. In contrast, the symmetry of the simple Z-band in fish myotomal white muscle, which in longitudinal sections has the appearance of a single zigzag structure, is p121 (Luther, P. K. (1991), J. Cell Biol. 113, 1043-1055).