Symmetry adaptation of configuration basis in MCSCF method

Summary A novel approach of space symmetry adaptation is developed for multiconfigurational (MC) functions in fully optimized reaction space and complete active space SCF calculations. The bonded tableau and two box symmetric tableau are basic representations (rep) of configuration functions; the group symmetric localized orbitals are used as one-electron orbitals. The method is proposed for generating a complete and orthonormal set of MC single excited functions. The redundant variable in MCSCF can be eliminated by symmetry adaptation.     

Towards the Development and Applications of Manifestly Spin-free Multi-reference Coupled Electron-pair Approximation-like Methods: A State Specific Approach

As a practical tool of being applicable to bigger molecules, a full-blown state-specific multi-reference coupled cluster formalism developed by us (Mahapatra et al. in J Chem Phys 110:6171, 1999) would be rather demanding computationally, and it is worthwhile to look for physically motivated approximation schemes which capture a substantial portion of the correlation of the full-blown theory. In this spirit, we have recently proposed coupled electron-pair approximation (CEPA)-like various approximants to the parent spin-adapted state-specific multi-reference coupled cluster (SS-MRCC) theory which depend on the inclusion of EPV terms to various degree. Here, the space of excitations is confined to the first order interactive virtual space generated by the cluster operator, but the EPV terms are included exactly. We call them spin-free state specific multi-reference CERA (SS-MRCEPA) theories. They work within the complete active space (CAS) and have been found to be very effective in bypassing the intruders, similar in performance to that of the parent SS-MRCC theory. The spin-adaptation of the working equations of both the SS-MRCC and the CEPA-like approximants is a non-trivial exercise. In this paper, we delineate briefly the essentials of a spin-free formulation of the SS-MRCC and SS-MRCEPA theories. This allows us to include open-shell configuration state functions (CSF) in the CAS. We consider three variants of SS-MRCEPA method. Two are explicitly orbital invariant: (1) SS-MRCEPA(0), a purely lineralized version of the SS-MRCC theory, (2) SS-MRCEPA(I), which includes all the EPV terms explicitly and exactly in an orbital invariant manner and (3) the SS-MRCEPA(D), which emerges when we keep only the diagonal terms of a set of dressed operators in the working equations. Unlike the first two, the third version is not invariant under the orbital transformation within the set of doubly occupied core, valence and virtual orbitals. The SS-MRCEPA methods produce very encouraging results as was evidenced in the applications on the computation of potential energy surfaces for the ground states of LiH and HF molecules.     

Spectral image adaptation and visual experience of DBA/PMMA

High resolution S0-->Sn and T1-->Tn electronic absorptions and B-type delayed fluorescence of 1,2,7,8-dibenzanthracene in polymethylmethacrylate (PMMA) were experimentally observed by flash and laser flash photolysis technique. Dibenzanthracene (hereafter DBA) molecules were excited in a two-step process. In the first step, an excited singlet is created, which undergoes intersystem crossing to triplet state, then T-T absorption creates an excited triplet dibenzanthracene molecule, which returns to the first excited singlet level by intersystem crossing. The re-created first excited singlet of dibenzanthracene decays back to the ground state by emitting B-type of delayed fluorescence, which was observed at the same emission band of prompt (normal) fluorescence, and R-, E-, P-types of delayed fluorescences. For normal fluorescence, S1 state is decaying to S0 ground state. For E- and P-type of delayed fluorescences, T1 state is decaying to S0 via S1 state, and for B-type of delayed fluorescence, T2 state is decaying to S0 via S1 state. The spectrum image showing the absorption/emission bands mentioned was also examined by image processing techniques in order to improve the visual experience of each band by localizing to a specific region of interest (ROI). Experimental results illustrate how the exact location of emission/absorption bands was clearly extracted from the spectral image and further improvements in the visual detection of absorption/emission bands.     

Novel calibration and color adaptation schemes in three-fringe RGB photoelasticity

Isochromatic demodulation in digital photoelasticity using RGB calibration is a two step process. The first step involves the construction of a look-up table (LUT) from a calibration experiment. In the second step, isochromatic data is demodulated by matching the colors of an analysis image with the colors existing in the LUT. As actual test and calibration experiment tint conditions vary due to different sources, color adaptation techniques for modifying an existing primary LUT are employed. However, the primary LUT is still generated from bending experiments. In this paper, RGB demodulation based on a theoretically constructed LUT has been attempted to exploit the advantages of color adaptation schemes. Thereby, the experimental mode of LUT generation and some uncertainties therein can be minimized. Additionally, a new color adaptation algorithm is proposed using quadratic Lagrangian interpolation polynomials, which is numerically better than the two-point linear interpolations available in the literature. The new calibration and color adaptation schemes are validated and applied to demodulate fringe orders in live models and stress frozen slices.     

Support vector machine with a Pearson VII function kernel for discriminating halophilic and non-halophilic proteins

Understanding of proteins adaptive to hypersaline environment and identifying them is a challenging task and would help to design stable proteins. Here, we have systematically analyzed the normalized amino acid compositions of 2121 halophilic and 2400 non-halophilic proteins. The results showed that halophilic protein contained more Asp at the expense of Lys, Ile, Cys and Met, fewer small and hydrophobic residues, and showed a large excess of acidic over basic amino acids. Then, we introduce a support vector machine method to discriminate the halophilic and non-halophilic proteins, by using a novel Pearson VII universal function based kernel. In the three validation check methods, it achieved an overall accuracy of 97.7%, 91.7% and 86.9% and outperformed other machine learning algorithms. We also address the influence of protein size on prediction accuracy and found the worse performance for small size proteins might be some significant residues (Cys and Lys) were missing in the proteins.     

An unstructured finite‐volume method for coupled models of suspended sediment and bed load transport in shallow‐water flows

The aim of this work is to develop a well‐balanced finite‐volume method for the accurate numerical solution of the equations governing suspended sediment and bed load transport in two‐dimensional shallow‐water flows. The modelling system consists of three coupled model components: (i) the shallow‐water equations for the hydrodynamical model; (ii) a transport equation for the dispersion of suspended sediments; and (iii) an Exner equation for the morphodynamics. These coupled models form a hyperbolic system of conservation laws with source terms. The proposed finite‐volume method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe's scheme using the sign of the Jacobian matrix in the coupled system. A well‐balanced discretization is used for the treatment of source terms. In this paper, we also employ an adaptive procedure in the finite‐volume method by monitoring the concentration of suspended sediments in the computational domain during its transport process. The method uses unstructured meshes and incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep sediment concentrations and bed load gradients that may form in the approximate solutions. Details are given on the implementation of the method, and numerical results are presented for two idealized test cases, which demonstrate the accuracy and robustness of the method and its applicability in predicting dam‐break flows over erodible sediment beds. The method is also applied to a sediment transport problem in the Nador lagoon.Copyright © 2013 John Wiley & Sons, Ltd.     

An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem. Several variants of the new condition are obtained. Based on one of them, two metric tensors for use in anisotropic mesh generation are developed to account for DMP satisfaction and the combination of DMP satisfaction and mesh adaptivity. Numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors.     

An accurate anisotropic adaptation method for solving the level set advection equation

In the present paper, a mesh adaptation process for solving the advection equation on a fully unstructured computational mesh is introduced, with a particular interest in the case it implicitly describes an evolving surface. This process mainly relies on a numerical scheme based on the method of characteristics. However, low order, this scheme lends itself to a thorough analysis on the theoretical side. It gives rise to an anisotropic error estimate which enjoys a very natural interpretation in terms of the Hausdorff distance between the exact and approximated surfaces. The computational mesh is then adapted according to the metric supplied by this estimate. The whole process enjoys a good accuracy as far as the interface resolution is concerned. Some numerical features are discussed and several classical examples are presented and commented in two or three dimensions. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive finite volume methods with well‐balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam‐break flood (France, 1959)

The simulation of advancing flood waves over rugged topography, by solving the shallow‐water equations with well‐balanced high‐resolution finite volume methods and block‐structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block‐structured AMR makes large‐scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet–dry fronts and non‐stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well‐balanced Riemann solver for inundation and general (non‐stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well‐balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam‐break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEO CLAW , a subset of the open‐source CLAWPACK software. All the software is freely available at www.clawpack.org . Published in 2010 by John Wiley & Sons, Ltd.     

Analysis of low-abundance proteins using the proteomic reactor with pH fractionation

We developed a new method consisting of the proteomic reactor coupled with step pH fractionation for the analysis of low-abundance proteins from minute amount of sample. These new reactors were implemented using both SAX and SCX materials. The pH fractions from the SAX reactor provided higher peptide and protein identification than SCX reactor and conventional solution digestion. Interestingly, the physical characteristics (pI, molecular weight, missed cleavage site and grand average hydrophobicity (GRAVY) index, and number of acid and basic amino acid) of the peptides obtained from the SAX and SCX proteomic reactors are drastically different. Furthermore, nearly half of the peptides observed from the pH fractionations from the SAX reactor are of low abundance while only 22% low-abundance proteins are observed with conventional in-solution digestion following 2D LC-MS/MS analysis.