A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

High‐efficiency polymer solar cells based on phenylenevinylene copolymer with BF2‐azopyrrole complex and CN‐PC70BM with solvent additive

Power conversion efficiency (PCE) of phenylenevinylene‐based copolymer with BF₂ azopyrrole complex (PB)/modified PC₇₀BM, that is, CN‐PC₇₀BM bulk heterojunction solar cells improves from 2.16 to 4.90% using a processing additive and drying condition. The results demonstrate that a processing additive and drying condition provides an effective means to control both the surface roughness and finer interpenetrating networks to enhance the exciton dissociation into free charge carriers, charge transportation, and collection. Taking into the account of simple device fabrication process without thermal annealing, the PCE of the polymer solar cell can further improved by chloronapthalene (CN) additive under the fast drying condition. The average carrier lifetimes extracted from the impedance spectra and found to correlate with measured PCEs. At short circuit conditions and illumination, the average charge carrier lifetime was found vary from 16.8 to 32 μs with power conversion efficiencies ranging from 3.0 to 4.9%. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

STABILITY ANALYSIS OF A CAPACITIVE FGM MICRO-BEAM USING MODIFIED COUPLE STRESS THEORY

Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.     

Cross section of the impact single ionization of B2＋ by H＋

The ionization process of B2+ by H+ impact is studied using the continuum-distorted-wave eikonal-initial-state (CDW-EIS) method and the modified free electron peak approximation (M-FEPA), respectively. Total, single-, and double- differential cross sections from 1s and 2s orbitals are presented for the energy range from 10 keV/u to 10 MeV/u. Comparison between the results from the two methods demonstrates that the total and single-differential cross sections for the high-energy incident projectile case can be well evaluated using the simple M-FEPA model. Moreover, the M-FEPA model reproduces the essential features of the binary-encounter (BE) bump in the double-differential cross sections. Thus, the BE ionization mechanism is discussed in detail by adopting the M-FEPA model. In particular, the double- and single-differential cross sections from the 2s orbital show a high-energy hip, which is different from those from the 1s orbital. Based on Ref. [1], the Compton profiles of B2+ for 1s and 2s orbitals are given, and the hips in DDCS and SDCS from the 2s orbital are explained.     

Molecular Dynamics Simulation and Density Functional Theory Study of Chemisorption of Propranolol Optical Isomers on a Uracil‐modified Carbon Paste Electrode

To reveal the nature of the interaction of the optical isomers of propranolol with the surface of carbon paste electrodes modified by uracil, we performed a combined computational and experimental study. Our study comprised the different modes of complexation between propranolol and uracil molecules covering the carbon paste electrode within two approaches: molecular dynamics simulation (MD ) and quantum mechanics (QM) modeling. A graphene layer was used as a model of the carbon paste electrode. The computations showed that uracil modification of the carbon paste electrode surface enhanced the selectivity toward the D‐isomer of propranolol as compared to the unmodified case. These theoretical results agree with our voltammetric measurements.     

Synthesis of 2′‐Amino‐2′‐deoxyuridine Modified by 1,8‐Naphthalimide

A simple and efficient synthetic route of 2′‐amino‐2′‐deoxyuridine was studied. 2′‐Amino‐2′‐deoxyuridine was incorporated into 1,8‐naphthalimides in the 2′‐position of 2′‐sugar via linking arms of different lengths. A convenient method for the synthesis of the conjugates was adopted.     

关于改性碳酸钙性能测试方法的探讨

详细介绍了力学性能测试、松散堆积密度法、萃取法测接枝率等改性碳酸钙性能测试法。讨论发现,3种方法的测试结果完全吻合,由此可证明松散堆积密度法、萃取法测接枝率也是行之有效的测试新方法。