On a hidden symmetry of quantum harmonic oscillators

We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg uncertainty principle is presented.     

Stable,High‐Molecular‐Weight Poly(phthalaldehyde)

Low ceiling temperature, thermodynamically unstable polymers have been troublesome to synthesize and keep stable during storage. In this study, stable poly(phthalaldehyde) has been synthesized with BF₃‐OEt₂ catalyst. The role of BF₃ in the polymerization is described. The interaction of BF₃ with the monomer is described and used to maximize the yield and molecular weight of poly(phthalaldehyde). Various Lewis acids were used to investigate the effect of catalyst acidity on poly(phthalaldehyde) chain growth. In situ nuclear magnetic resonance was used to identify possible interactions formed between BF₃ and phthalaldehyde monomer and polymer. The molecular weight of the polymer tracks with polymerization yield. The ambient temperature stability of poly(phthalaldehyde) was investigated and the storage life of the polymer has been improved. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 55, 1166–1172     

Full rate constant matrix contraction method for obtaining branching ratio of unimolecular decomposition

The branching ratio of unimolecular decomposition can be evaluated by solving the rate equations. Recent advances in automated reaction path search methods have enabled efficient construction of the rate equations based on quantum chemical calculations. However, it is still difficult to solve the rate equations composed of hundreds or more elementary steps. This problem is especially serious when elementary steps that occur in highly different timescales coexist. In this article, we introduce an efficient approach to obtain the branching ratio from a given set of rate equations. It has been derived from a recently proposed rate constant matrix contraction (RCMC) method, and termed full‐RCMC (f‐RCMC). The f‐RCMC gives the branching ratio without solving the rate equations. Its performance was tested numerically for unimolecular decomposition of C₃H₅ and C₄H₅. Branching ratios obtained by the f‐RCMC precisely reproduced the values obtained by numerically solving the rate equations. It took about 95 h to solve the rate equations of C₄H₅ consisting of 234 elementary steps. In contrast, the f‐RCMC gave the branching ratio in less than 1 s. The f‐RCMC would thus be an efficient alternative of the conventional kinetic simulation approach. © 2016 Wiley Periodicals, Inc.     

On the free vibration response of rectangular plates,partially supported on elastic foundation

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind.     

Third‐order WENO scheme with a new smoothness indicator

In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.     

Mechanistic model for deformation of polymer nanocomposite melts under large amplitude shear

We report the mechanical response of a model nanocomposite system of poly(styrene) (PS)-silica to large-amplitude oscillatory shear deformations. Nonlinear behavior of PS nanocomposites is discussed with the changes in particle dispersion upon deformation to provide a complete physical picture of their mechanical properties. The elastic stresses for the particle and polymer are resolved by decomposing the total stress into its purely elastic and viscous components for composites at different strain levels within a cycle of deformation. We propose a mechanistic model which captures the deformation of particles and polymer networks at small and large strains, respectively. We show, for the first time, that chain stretching in a polymer nanocomposite obtained in large amplitude oscillatory deformation is in good agreement with the nonlinear chain deformation theory of polymeric networks. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Intermolecular Charge-Transfer Interactions Facilitate Two-Photon Absorption in Styrylpyridine–Tetracyanobenzene Cocrystals

Cocrystals of 4-styrylpyridine and 1,2,4,5-tetracyanobenzene were successfully prepared by supramolecular self-assembly. Donor–acceptor interactions between the molecular components are the main driving force for self-assembly and contribute to intermolecular charge transfer. The cocrystals possess two-photon absorption properties that are not observed in the individual components; suggesting that two-photon absorption originates from intermolecular charge-transfer interactions in the donor–acceptor system. The origin of two-photon absorption in multichromophore systems remains under-researched; thus, the system offers a rare demonstration of two-photon absorption by cocrystallization. Cocrystal engineering may facilitate further design and development of novel materials for nonlinear optical and optoelectronic applications.     

Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique

We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.