Symmetry-based Approach Research Articles

Double-resonant Raman scattering with optical and acoustic phonons in carbon nanotubes

We analyze and assign two low-intensity, double-resonant Raman bands at around 1950 ${\mathrm{cm}}^{\ensuremath{-}1}$ and 2450 ${\mathrm{cm}}^{\ensuremath{-}1}$ in carbon nanotube ensembles. We present Raman spectra of a high-pressure carbon monoxide sample for laser energies in the visible range. By using density functional theory plus zone folding, we simulate both combination modes for various excitation energies with respect to the chiral-index distribution of carbon nanotubes in the sample. For a comparison, double-resonant Raman spectra of single carbon nanotubes are also modeled within a symmetry-based nonorthogonal tight-binding approach, resulting in a different assignment of the 1950-${\mathrm{cm}}^{\ensuremath{-}1}$ band. Apparent discrepancies in the assignments are discussed in the article.

Partial dynamical symmetries and shape coexistence in nuclei

We present a symmetry-based approach for shape coexistence in nuclei, founded on the concept of partial dynamical symmetry (PDS). The latter corresponds to the situation where only selected states (or bands of states) of the coexisting configurations preserve the symmetry while other states are mixed. We construct explicitly critical-point Hamiltonians with two or three PDSs of the types U(5), SU(3), and SO(6), appropriate to double or triple coexistence of spherical, prolate, oblate and γ-soft deformed shapes, respectively. In each case, we analyze the topology of the energy surface with multiple minima and corresponding normal modes. Characteristic features and symmetry attributes of the quantum spectra and wave functions are discussed. Analytic expressions for quadrupole moments and E2 rates involving the remaining solvable states are derived and isomeric states are identified by means of selection rules.

Analysis of the Electronic Structure of the Special Pair of a Bacterial Photosynthetic Reaction Center by 13 C Photochemically Induced Dynamic Nuclear Polarization Magic-Angle Spinning NMR Using a Double-Quantum Axis.

The origin of the functional symmetry break in bacterial photosynthesis challenges since several decades. Although structurally very similar, the two branches of cofactors in the reaction center (RC) protein complex act very differently. Upon photochemical excitation, an electron is transported along one branch, while the other remains inactive. Photochemically induced dynamic nuclear polarization (photo-CIDNP) magic-angle spinning (MAS) 13 C NMR revealed that the two bacteriochlorophyll cofactors forming the "Special Pair" donor dimer are already well distinguished in the electronic ground state. These previous studies are relying solely on 13 C-13 C correlation experiments as radio-frequency-driven recoupling (RFDR) and dipolar-assisted rotational resonance (DARR). Obviously, the chemical-shift assignment is difficult in a dimer of tetrapyrrole macrocycles, having eight pyrrole rings of similar chemical shifts. To overcome this problem, an INADEQUATE type of experiment using a POST C7 symmetry-based approach is applied to selectively isotope-labeled bacterial RC of Rhodobacter (R.) sphaeroides wild type (WT). We, therefore, were able to distinguish unresolved sites of the macromolecular dimer. The obtained chemical-shift pattern is in-line with a concentric assembly of negative charge within the common center of the Special Pair supermolecule in the electronic ground state.

Quantifying wall turbulence via a symmetry approach: a Lie group theory

First-principle-based prediction of mean-flow quantities of wall-bounded turbulent flows (channel, pipe and turbulent boundary layer (TBL)) is of great importance from both physics and engineering standpoints. Here we present a symmetry-based approach which yields analytical expressions for the mean-velocity profile (MVP) from a Lie-group analysis. After verifying the dilatation-group invariance of the Reynolds averaged Navier–Stokes (RANS) equation in the presence of a wall, we depart from previous Lie-group studies of wall turbulence by selecting a stress length function as a similarity variable. We argue that this stress length function characterizes the symmetry property of wall flows having a simple dilatation-invariant form. Three kinds of (local) invariant forms of the length function are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall and hence also the MVP, using the mean-momentum equation. In particular, based on this multi-layer formula, we obtain analytical expressions for the (universal) wall function and separate wake functions for pipe and channel, which are validated by data from direct numerical simulations (DNS). In conclusion, an analytical expression for the entire MVP of wall turbulence, beyond the log law or power law, is developed in this paper and the theory can be used to describe the mean turbulent kinetic-energy distribution, as well as a variety of boundary conditions such as pressure gradient, wall roughness, buoyancy, etc. where the dilatation-group invariance is valid in the wall-normal direction.

Parametric Shape Grammar Formalism for Moorish Geometric Design Analysis and Generation

The goal of this article is to propose a modeling method to automatically generate original and new forms of periodic Moorish geometric patterns. The proposed method is based on the symmetry-based approach and the shape grammar formalism. The symmetry-based approach consists of constructing a periodic pattern by using isometric transformations of its template motif. The main contribution of this article is to propose a parametric shape grammar method to generate the template motif. The process used consists first in identifying the shapes vocabulary characterizing the Moorish style. By identifying its common features by the analysis of a dataset of historical Moorish patterns, parametric shape grammar (PSG) rules are then determined. Furthermore, the use of PSGs implies additional mechanisms, such as the consideration of suitable constraints and goals. These mechanisms are imposed by the grid, which is the underlying geometric structure used traditionally by artisans to design sophisticated geometric patterns. The performance of the proposed method is measured by its capability to create original and new motifs of periodic Moorish patterns. This method preserves the authenticity of the style considered, because the generated patterns follow a parametric shape grammar based on a priori domain knowledge and extract one from representative images of Moorish style.

Symmetry-based approach to oligostilbenoids: Rapid entry to viniferifuran, shoreaphenol, malibatol A, and diptoindonesin G.

The recognition of the local symmetric image within benzofuran-based natural oligostilbenoids guided us to design a modular synthetic approach to these molecules by utilizing a three-step sequence consisting of Sonogashira coupling, iodocyclization, and Suzuki coupling. During our synthesis, the relative reactivities of ester, aldehyde, and alkoxy groups on the same aryl ring toward the neighboring alkyne in the iodine-mediated cyclization reactions were explored. Starting from the symmetrical 3,5-dimethoxybenzyl alcohol, this route allowed rapid access to 2,3-diarylbenzofuran, a key intermediate to several oligostilbenoid natural products, in good overall yields.

Engineering Protein Self-Assembly: A New Approach for the Design of Octahedral Cages.

A new symmetry-based approach allowed the self-assembly of an octahedral protein nanostructure. C3 trimeric and C4 tetrameric oligomerization domains can be combined in an engineered protein to direct assembly into a desired object. This work might provide the basis for a more general and flexible strategy to control protein self-assembly.

Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches.

In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.

Algebraic benchmark for prolate-oblate coexistence in nuclei

We present a symmetry-based approach for prolate-oblate and spherical-prolate-oblate shape coexistence, in the framework of the interacting boson model of nuclei. The proposed Hamiltonian conserves the SU(3) and $\overline{\rm SU(3)}$ symmetry for the prolate and oblate ground bands and the U(5) symmetry for selected spherical states. Analytic expressions for quadrupole moments and $E2$ rates involving these states are derived and isomeric states are identified by means of selection rules.

Dirac cones beyond the honeycomb lattice: A symmetry-based approach

Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensional Dirac systems based on the space groups, and discuss our findings within the context of a minimal two-band model. In particular, we show that the emergence of massless Dirac fermions can be attributed to the mirror symmetries of the materials. Moreover, we uncover several novel Dirac systems that have up to twelve inequivalent Dirac cones, and show that these can be realized in (twisted) bilayers. Hereby, we obtain systems with an emergent SU(2N) valley symmetry with N=1,2,4,6,8,12. Our results pave the way to engineer different Dirac systems, besides providing a simple and unified description of materials ranging from square- and $\beta$-graphynes, to Pmmn-Boron, TiB$_2$, phosphorene, and anisotropic graphene.

Some tree-level string amplitudes in the NSR formalism

We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric $F^4$ effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.

应用结构系综理论发展壁湍流工程湍流模型

One of the greatest challenges in computational modeling of real engineering flows is to derive physically sound turbulence models and to determine their (numerous) coefficients from the understanding of turbulence physics, which has been a bottleneck in turbulence studies for several decades for the lack of a sound theoretical framework. Here, we present a new symmetry-based approach, called structural ensemble dynamics (SED), and apply it to develop new turbulence models. The SED theory focuses on revealing the symmetry properties of wall-bounded flows including channel, pipe, turbulent boundary layer, RB convection, etc. We propose a concept of order function which preserves the dilation invariance due to the presence of wall, yielding a new parameterization for mean profiles in terms of physical multi-layer structure parameters (thickness, scaling, etc.). The SED can be applied to study the Reynolds-averaged Navier-Stokes equation with turbulence models whose defect is easily revealed under the multi-layer picture. We report here the improvement of the k - w model for pipe flow modeling, as well as the definition of a new algebraic model for compressible turbulent boundary layer (CTBL) modeling. The modified k-ω model, the so-called SED- k - w model, has achieved, for the first time, accurate prediction of both mean velocity and (streamwise) kinetic energy for a wide range of Reynolds number, with a 99% accuracy when compared to the Princeton experimental data. In addition, this study has laid a solid support to the universal Karman constant 0.45. Moreover, it points out the existence of a meso-layer with anomaly in energy dissipation, which explains both the outer peak and the approximate logarithmic law in the kinetic energy profile. Secondly, we report a new algebraic model, SED-SL model, which performs clearly superior in both accuracy and simplicity to the Baldwin & Lomax model for the modeling of CTBL. The SED-based models have two distinct features: the first is its accurate determination of the multi-layer structure, being the origin of the high accuracy, and the second is its physical description of the parameters in terms of local scaling and thickness. The latter makes possible of raising the accuracy of CFD models by considering the spatial variation of the physical multi-layer structure parameters in complex flows.

Automatic localization of the anterior commissure, posterior commissure, and midsagittal plane in MRI scans using regression forests.

Localizing the anterior and posterior commissures (AC/PC) and the midsagittal plane (MSP) is crucial in stereotactic and functional neurosurgery, human brain mapping, and medical image processing. We present a learning-based method for automatic and efficient localization of these landmarks and the plane using regression forests. Given a point in an image, we first extract a set of multiscale long-range contextual features. We then build random forests models to learn a nonlinear relationship between these features and the probability of the point being a landmark or in the plane. Three-stage coarse-to-fine models are trained for the AC, PC, and MSP separately using downsampled by 4, downsampled by 2, and the original images. Localization is performed hierarchically, starting with a rough estimation that is progressively refined. We evaluate our method using a leave-one-out approach with 100 clinical T1-weighted images and compare it to state-of-the-art methods including an atlas-based approach with six nonrigid registration algorithms and a model-based approach for the AC and PC, and a global symmetry-based approach for the MSP. Our method results in an overall error of 0.55 ±0.30 mm for AC, 0.56 ±0.28 mm for PC, 1.08(°) ±0.66 in the plane's normal direction, and 1.22 ±0.73 voxels in average distance for MSP; it performs significantly better than four registration algorithms and the model-based method for AC and PC, and the global symmetry-based method for MSP. We also evaluate the sensitivity of our method to image quality and parameter values. We show that it is robust to asymmetry, noise, and rotation. Computation time is 25s.

Spatially flat matter-dominated universe filled with barotropic causal bulk viscous fluid: a symmetry-based approach

We have studied a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model with an additional assumption that the universe is filled with barotropic causal bulk viscous fluid. The bulk viscous coefficient of the fluid is related to the energy density and relaxation time by the relation . We have used a truncated version of the transport equation for the viscous pressure. The expansion rate of such a spatially flat FLRW universe is governed by the well-known modified Painlevé–Ince equation. We find that the Lie symmetry corresponding to scale invariance gives the power-law solution for this model equation from invariant curve condition. For the value of , our result satisfies the present experimental value of the deceleration parameter (q) for . The result obtained for the relaxation time which is of the order of the Hubble time supports the necessary condition for successful inflation. Our study not only shows the role of the bulk viscosity for the present accelerating expansion but also predicts an age of around , which solves the age problem of the present universe.

Tunneling splitting in double-proton transfer: direct diagonalization results for porphycene.

Zero-point and excited level splittings due to double-proton tunneling are calculated for porphycene and the results are compared with experiment. The calculation makes use of a multidimensional imaginary-mode Hamiltonian, diagonalized directly by an effective reduction of its dimensionality. Porphycene has a complex potential energy surface with nine stationary configurations that allow a variety of tunneling paths, many of which include classically accessible regions. A symmetry-based approach is used to show that the zero-point level, although located above the cis minimum, corresponds to concerted tunneling along a direct trans - trans path; a corresponding cis - cis path is predicted at higher energy. This supports the conclusion of a previous paper [Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007)] based on the instanton approach to a model Hamiltonian of correlated double-proton transfer. A multidimensional tunneling Hamiltonian is then generated, based on a double-minimum potential along the coordinate of concerted proton motion, which is newly evaluated at the RI-CC2/cc-pVTZ level of theory. To make it suitable for diagonalization, its dimensionality is reduced by treating fast weakly coupled modes in the adiabatic approximation. This results in a coordinate-dependent mass of tunneling, which is included in a unique Hermitian form into the kinetic energy operator. The reduced Hamiltonian contains three symmetric and one antisymmetric mode coupled to the tunneling mode and is diagonalized by a modified Jacobi-Davidson algorithm implemented in the Jadamilu software for sparse matrices. The results are in satisfactory agreement with the observed splitting of the zero-point level and several vibrational fundamentals after a partial reassignment, imposed by recently derived selection rules. They also agree well with instanton calculations based on the same Hamiltonian.

Note on Kerr/CFT correspondence in a first order formalism

In symmetry-based approaches to black hole entropy, we calculate the central charge of the Virasoro algebra in the first order formulation of gravity for both Palatini and Holst actions. In these calculations, we make use of the near-horizon extremal Kerr metric and the Kerr/conformal field theory correspondence. For the Palatini action the results obtained in the second order formulation are reproduced. We also argue that the Holst term does not contribute to the charge algebra no matter what geometry/boundary conditions one is considering.

Symmetry-based approach to ground-state properties of the one-dimensional negative-U Bose–Hubbard trimer model

It is shown that the ground state of the one-dimensional negative-U three-site Bose–Hubbard (trimer) model with periodic (boundary) condition or for a closed chain can be solved almost exactly within a small symmetric subspace with a few boson-trines through an analysis of the percentage of the boson-trines in the ground state. It is also shown that there is a sudden increase of the boson-trine content of the ground state near the critical point of the quantum phase transition, which may be used as an effective order parameter to study the phase transition of the model. The ground-state energy per particle and the entanglement measure with the variation of the control parameter are also analyzed to show their transitional behavior.

Generic miniband structure of graphene on a hexagonal substrate

Using a general symmetry-based approach, we provide a classification of generic miniband structures for electrons in graphene placed on substrates with the hexagonal Bravais symmetry. In particular, we identify conditions at which the first moir\'e miniband is separated from the rest of the spectrum by either one or a group of three isolated mini Dirac points and is not obscured by dispersion surfaces coming from other minibands. In such cases the Hall coefficient exhibits two distinct alternations of its sign as a function of charge carrier density.

Symmetry-based approach to parametrization of embedded-atom-method interatomic potentials

A new approach to the parametrization of the Embedded Atom Method (EAM) potentials describing interatomic interactions in metal crystals has been presented. The proposed method requires that the EAM model correctly reproduces elementary strain processes resulting from the spectral decomposition of the elasticity tensor. Then, an arbitrary process of small strain of the considered crystal will proceed in accordance with the experiment. The parametrization conditions obtained in this way take a particularly simple form thanks to using crystal symmetry at two levels: continuum and atomistic one. At the first level, the symmetry determines the elementary processes and at the second one – it enables the simplification of the formulated parametrization conditions by applying the orthogonality relationships in the point group of the considered crystal. Under the proposed approach, the parametrization equations have been formulated for cubic crystals. The obtained relationships have been used to examine existing parameterizations of the Rosato–Guillope–Legrand potential for a copper crystal and subsequently to determine the individual set of parameters which gives results more consistent with the experimental data.

Algorithm and Architecture for N-D Vector Cross-Product Computation

Multidimensional vector cross-product has not been studied from the perspective of signal processing so far to the best of our knowledge and hence no effort has been made to develop any generalized algorithm for its hardware implementation. In this paper firstly, we identify the application domain of cross-product in signal processing and then introduce a novel recursive algorithm for generalized nD cross-product computation considering three dimensional (3D) cross-product as the fundamental operation. Subsequently a generalized scheme for architecture implementation for nD cross-product is proposed based on this algorithm. Secondly, we show that if 4D cross-product is used as the fundamental operation for formulating nD cross-product problem, then exploiting the inherent mathematical symmetry of 4D cross-product it is possible to reduce the total hardware cost of nD cross-product significantly at the architecture level (symmetry-based approach). Mathematical models for hardware complexity and operational delay have been formulated both for the generalized and symmetry-based approaches.