Stabilization of a high energy molecular conformation by specific intermolecular forces, a novel planar benzylideneaniline system

The system containing six benzylideneanilines (BA) has been studied: Group 1:

2D Burgers equation with large Reynolds number using POD/DEIM and calibration

Model order reduction of the two‐dimensional Burgers equation is investigated. The mathematical formulation of POD/discrete empirical interpolation method (DEIM)‐reduced order model (ROM) is derived based on the Galerkin projection and DEIM from the existing high fidelity‐implicit finite‐difference full model. For validation, we numerically compared the POD ROM, POD/DEIM, and the full model in two cases of Re = 100 and Re = 1000, respectively. We found that the POD/DEIM ROM leads to a speed‐up of CPU time by a factor of O(10). The computational stability of POD/DEIM ROM is maintained by means of a careful selection of POD modes and the DEIM interpolation points. The solution of POD/DEIM in the case of Re = 1000 has an accuracy with error O(10^?3) versus O(10^?4) in the case of Re = 100 when compared with the high fidelity model. For this turbulent flow, a closure model consisting of a Tikhonov regularization is carried out in order to recover the missing information and is developed to account for the small‐scale dissipation effect of the truncated POD modes. It is shown that the computational results of this calibrated ROM exhibit considerable agreement with the high fidelity model, which implies the efficiency of the closure model used. Copyright © 2016 John Wiley & Sons, Ltd.     

On Estimation of Temperature Uncertainty Using the Second Order Adjoint Problem

The uncertainty of temperature prediction from the heat flux error is estimated using first and second order adjoint equations. The adjoint codes developed for the inverse heat transfer problems provide the uncertainty estimation for the corresponding forward problems. Numerical tests corroborate the feasibility of fast uncertainty estimation using Hessian maximum eigenvalue obtained via second order adjoint equations.     

An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids

In this article, we describe a non‐intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non‐intrusive reduced‐order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non‐intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hypersurfaces representing the reduced‐porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high‐fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude. Copyright © 2016 John Wiley & Sons, Ltd.     

A study of dipolar interactions and dynamic processes of water molecules in tendon by 1H and 2H homonuclear and heteronuclear multiple-quantum-filtered NMR spectroscopy

The effect of proton exchange on the measurement of 1H-1H, 1H-2H, and 2H-2H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the 1H-1H and 1H-2H residual dipolar interactions and the proton exchange rate at a temperature of 24 degrees C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24 degrees C were 300 and 50 Hz and 3000 s-1, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5 degrees C, where the spectra of the H2O molecules were well resolved, so that the 1H-1H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5 degrees C, where the proton exchange was in the intermediate regime for the 1H-2H dipolar interaction, confirmed the result obtained at 24 degrees C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T2) depend on the orientation as the square of the second-rank Legendre polynomial.     

Detection and characterization of boric acid and borate ion binding to cytochrome c using multiple quantum filtered NMR

The application of multiple quantum filtered (MQF) NMR to the identification and characterization of the binding of ligands containing quadrupolar nuclei to proteins is demonstrated. Using relaxation times measured by MQF NMR multiple binding of boric acid and borate ion to ferri and ferrocytochrome c was detected. Borate ion was found to have two different binding sites. One of them was in slow exchange, k(diss) = 20 +/- 3 s(-1) at 5 degrees C and D(2)O solution, in agreement with previous findings by (1)H NMR (G. Taler et al., 1998, Inorg. Chim. Acta 273, 388-392). The triple quantum relaxation of the borate in this site was found to be governed by dipolar interaction corresponding to an average B-H distance of 2.06 +/- 0.07 A. Other, fast exchanging sites for borate and boric acid could be detected only by MQF NMR. The binding equilibrium constants at these sites at pH 9.7 were found to be 1800 +/- 200 M(-1) and 2.6 +/- 1.5 M(-1) for the borate ion and boric acid, respectively. Thus, detection of binding by MQF NMR proved to be sensitive to fast exchanging ligands as well as to very weak binding that could not be detected using conventional methods.     

Efficient broadband silicon-on-insulator grating coupler with low backreflection

We design and fabricate an efficient broadband grating coupler on a 400 nm thick silicon-on-insulator wafer. The measured coupling loss is 3 dB when coupling to a single-mode fiber at 1310 nm wavelength with TE polarization. The spectral FWHM and backreflection are determined to be 58 nm and -27 dB, respectively.     

A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere

In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

The Kuramoto–Sivashinsky equation plays an important role as a low‐dimensional prototype for complicated fluid dynamics systems having been studied due to its chaotic pattern forming behavior. Up to now, efforts to carry out data assimilation with this 1‐D model were restricted to variational adjoint methods domain and only Chorin and Krause (Proc. Natl. Acad. Sci. 2004; 101 (42):15013–15017) tested it using a sequential Bayesian filter approach. In this work we compare three sequential data assimilation methods namely the Kalman filter approach, the sequential Monte Carlo particle filter approach and the maximum likelihood ensemble filter methods. This comparison is to the best of our knowledge novel. We compare in detail their relative performance for both linear and nonlinear observation operators. The results of these sequential data assimilation tests are discussed and conclusions are drawn as to the suitability of these data assimilation methods in the presence of linear and nonlinear observation operators. Copyright © 2009 John Wiley & Sons, Ltd.