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.     

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.     

GW invariants relative to normal crossing divisors

In this paper we introduce a notion of symplectic normal crossing divisor V and define the GW invariant of a symplectic manifold X relative to such a divisor. Our definition includes normal crossing divisors from algebraic geometry. The invariants we define in this paper are key ingredients in symplectic sum type formulas for GW invariants, and extend those defined in our previous joint work with T.H. Parker [16], which covered the case V   was smooth. The main step is the construction of a compact moduli space of relatively stable maps into the pair (X,V)$(X,V)$ in the case V is a symplectic normal crossing divisor in X.     

Electromagnetic dissociation of relativistic 8B nuclei in nuclear track emulsion

Experimental data on fragmentation channels in peripheral interactions of ⁸B nuclei in nuclear track emulsions are presented. A detailed analysis made it possible to justify selections of events of the electromagnetic-dissociation process ⁸B → ⁷Be + p and to estimate its cross section. Events of ¹⁰C peripheral dissociation that were observed in the same exposure are described.     

Biosensors for phenol derivatives using biochemical signal amplification

Two different approaches, both exploiting two enzymes cooperative functioning, to enhance the sensitivity of tyrosinase (PPO) based biosensor for amperometric detection of phenols have been compared. For this purpose, one monoenzyme electrode (PPO) and two bienzyme electrodes (PPO and d-glucose dehydrogenase, GDH; PPO and horseradish peroxidase, HRP) were constructed using agar-agar gel as enzyme immobilization matrix. The biosensors responses for l-tyrosine detection were recorded at −50 mV versus saturated calomel electrode (SCE). The highest sensitivity (74 mA M⁻¹) was observed for the PPO-GDH couple, while that recorded for PPO-HRP couple system was only 32 times higher than that measured for monoenzyme electrode (0.01 mA M⁻¹). The ability of the PPO-, PPO-GDH-, PPO-HRP-based biosensors to assay phenols was demonstrated by quantitative determination of phenol, 1,2-dihydroxybenzene, 1,3-dihydroxybenzene, 1,4-dihydroxybenzene, 2-amino-3 (4-hydroxyphenyl) propanoic acid, 2-hydroxytoluene, 3-hydroxytoluene, 4-hydroxytoluene, 4-clorophenol, 3-clorophenol, 2-clorophenol, 4-hydroxybenzoic acid.     

Peripheral fragmentation of 8B nuclei in nuclear emulsion at an energy of 1.2 GeV per nucleon

The results obtained by studying the charge topology of fragments produced in the peripheral dissociation of relativistic ⁸B nuclei in emulsion are presented. Fifty-five events of the peripheral dissociation of a ⁸B nucleus in events where there was no production of target-nucleus fragments and mesons (“white stars”) were selected. A leading contribution of the ⁸B → ⁷Be + p mode, which has the lowest energy threshold, was revealed on the basis of these events. Information about the branching ratios for dissociation modes characterized by a higher multiplicity was obtained. The dissociation of the ⁷Be core in ⁸B bears resemblance to the dissociation of a free ⁷Be nucleus. The transverse-momentum distributions of fragments originating from the ⁸B → ⁷Be + p dissociation mode were obtained. For these distributions, a small mean value of 〈P*_T〉 = 52 ± 5 MeV/c in the c.m. frame suggests a low binding energy of the outer proton in the ⁸B nucleus. An indication of a strong azimuthal correlation of the fragments ⁷Be and p was found.     

Vibrational Spectra of Dimethyldithiophosphinate Anion: (CH3)2PS2

Abstract

The infrared and Raman spectra of dimethyldithiophosphinate anion (CH₃)₂PS₂ were measured and the vibrational modes for the anion complex were assigned. A Normal Coordinate Analysis in the Modified General Valence Force Field (MGVFF) approximation was carried out assuming C_2v symmetry. Ab Initio Calculations at RHF and MP2 level were also carried out for the anion geometry as well as for its frequencies, intensities and force constants.     

Spiroheterocyclic compounds: old stories with new outcomes

An efficient and straightforward method for the preparation of spirodiazine derivatives is reported which involves mild reaction conditions and easily accessible reactants. A new class of spiroazaheterocycles, spiro[pyrrolidine-pyrrolo[3,4-c]pyrroles], is obtained. A feasible explanation is given for the unexpected results obtained at high energy (high temperatures, MW and ultrasound irradiation).     

Differing Coordination Modes of (O‐Alkyl)‐p‐Ethoxyphenyldithiophosphonato Ligands in Copper(I), Silver(I) and Gold(I) Triphenylphosphine Complexes

The three (O‐methyl)‐p‐ethoxyphenyldithiophosphonato triphenylphosphine complexes of copper, silver and gold, [(Ph₃P)_nM{S₂P(OMe)C₆H₄OEt‐p}] (M = Cu, n = 2; M = Ag, Au, n = 1) investigated structurally by X‐ray diffraction exhibit remarkable structural differences. The copper compound is a four‐coordinate chelate monomer with Cu–S 2.4417(6) and 2.5048(6) Å; P–Cu–S 104.24(2)–114.01(2)°; Cu–S–P 82.49(3)° and 80.85(2)°. The silver compound is a cyclic dimer with bridging dithiophosphonato ligands and three‐coordinate silver atoms [Ag–S 2.5371(5) and 2.6867(5) Å; P–Ag–S 122.88(2)° and 122.17(2)°; Ag–S–P 89.32(2)° and 103.56(2)°]. The gold compound is monomeric with linear dicoordinate gold [Au–S 2.3218(6) Å; P–Au–S 177.72(2)°, Au–S–P 100.97(3)°].     

Conformational changes of strong polycations in the presence of divalent counterions and their influence upon the flocculation efficiency

The interaction between strong polycations, which possess the ammonium quaternary centers attached to an acrylic macromolecular chain derived from poly(N,N-dimethylaminoethyl methacrylate) (polycations Q_x), and divalent counterions was investigated by viscometry and turbidimetry. Conformational changes of polycations were influenced by the polycation charge density, counterion nature (SO₄²⁻ or S₂O₈²⁻) and concentration. The morphology of the polycation layers deposited onto silicon wafers has been studied by tapping mode atomic force microscopy, a strong influence of the polycation and ammonium persulfate concentration on the surface topography being observed. The optimum flocculation concentration of polycation decreased and the flocculation window increased in the presence of S₂O₈²⁻, in the destabilization of kaolin model dispersion. Removal of Congo Red from aqueous solution by the complex system formed between polycations and divalent counterions was also investigated. The behavior of polycations Q_x in separation processes was compared with that of one polycation containing 95 mol% N,N-dimethyl-2-hydroxypropyleneammonium chloride units in the backbone (PCA₅).