A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

The Hardy–Littlewood–Pólya inequality of majorization in the context of $$\mathbf {\omega }$$ – $$\textbf{m}$$ –star-convex functions

Aequationes mathematicae - The Hardy–Littlewood–Pólya inequality of majorization is extended for $$\mathbf {\omega }$$ – $$\textbf{m}$$ –star-convex functions to the...     

Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

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.     

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.     

Measurement of production date (age) of nanogram amount of uranium

JRC-Karlsruhe obtained a swipe sample from a highly enriched uranium seizure, which had taken place in 2011. Due to the very low amount of uranium (nanograms) a new method needed to be developed to determine the U production date (age). The particles on the swipe were collected on a pyrolytic graphite planchet using a vacuum impactor and they were subsequently leached with ccHNO₃. The “bulk” U isotopic composition (²³⁵U: 72.51?±?0.03 wt%) and the production date (December 1992?±?1 year) determined by MC-ICP-MS indicated that the material showed similarity with two other HEU cases seized earlier in Europe.

     

Supramolecular Systems from Natural Polymers and Maleic Polyelectrolytes

Summary: The formation of polyelectrolyte complexes by interaction between chitosan and maleic acid copolymers as strong/weak dibasic polyanions was investigated. The interaction between the sodium salt of maleic acid copolymers with styrene or vinyl acetate and the chitosan hydrochloride in aqueous solution was followed by potentiometric, conductometric and turbidimetric titration. The effect of the added low molecular salt on the complex formation was also investigated. The precipitated complexes were analyzed by FTIR spectroscopy and TG analysis. Preliminary layer-by-layer deposition experiments were performed to obtain thin films.