Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress. This instability is called the Rayleigh-Plateau instabilty. We consider the model developed by Spencer et ...     

Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.     

Broadband excitation pulses for high‐field solid‐state nuclear magnetic resonance spectroscopy

In nuclear magnetic resonance spectroscopy, experimental limits due to the radiofrequency transmitter and/or coil means that conventional radiofrequency pulses (“hard pulses”) are sometimes not sufficiently powerful to excite magnetization uniformly over a desired range of frequencies. Effects due to nonuniform excitation are most frequently encountered at high magnetic fields for nuclei with a large range of chemical shifts. Using optimal control theory, we have designed broadband excitation pulses that are suitable for solid‐state samples under magic‐angle‐spinning conditions. These pulses are easy to implement, robust to spinning frequency variations, and radiofrequency inhomogeneities, and only four times as long as a corresponding hard pulse. The utility of these pulses for uniformly exciting ¹³C nuclei is demonstrated on a 900 MHz (21.1 T) spectrometer. Copyright © 2012 John Wiley & Sons, Ltd.     

High magnetic field solid‐state NMR analyses by combining MAS,MQ‐MAS,homo‐nuclear and hetero‐nuclear correlation experiments

A general strategy of structural analysis of alumina silicate by combining various solid‐state NMR measurements such as single pulse, multi‐quantum magic angle spinning, double‐quantum homo‐nuclear correlation under magic angle spinning (DQ‐MAS), and cross‐polarization hetero‐nuclear correlation (CP‐HETCOR) was evaluated with the aid of high magnetic field NMR (800 MHz for ¹H Larmor frequency) by using anorthite as a model material. The high magnetic field greatly enhanced resolution of ²⁷Al in single pulse, DQ‐MAS, and even in triple‐quantum magic angle spinning NMR spectra. The spatial proximities through dipolar couplings were probed by the DQ‐MAS methods for homo‐nuclear correlations between both ²⁷Al–²⁷Al and ²⁹Si–²⁹Si and by CP‐HETCOR for hetero‐nuclear correlations between ²⁷Al–²⁹Si in the anorthite framework. By combining various NMR methodologies, we elucidated detailed spatial correlations among various aluminum and silicon species in anorthite that was hard to be determined using conventional analytical methods at low magnetic field. Moreover, the presented approach is applicable to analyze other alumina‐silicate minerals. Copyright © 2012 John Wiley & Sons, Ltd.     

Pressure dependent study of semiconductors using semiempirical equations of state

Abstract

Variation of bulk modulus of Si, Ge and GaAs with pressure is studied using four semiempirical equations of state, two of which being proposed very recently. Hence an expression for bulk modulus for arbitrary pressure for the semiconductors similar to Cohen's formula for zero pressure is arrived at. The applicability of these equations of state for the high pressure phases of Si and Ge is tested using the recent experimental and theoretical pressure-volume data of these phases.     

Existence analysis of an optimal shape design problem with non coercive state equation

In this paper, a shape optimization problem, modelling a welding process, governed by a second order non coercive PDE is considered. The well posedness of the shape optimal design problem is showed using the degree of Leray–Schauder. Then the existence of an optimal solution is proved.     

Ion Product of Pure Water Characterized by Physics-Based Water Model

Pure water has been characterized for nearly a century, by its dissociation into hydronium (H₃O)¹⁺ and hydroxide (HO)^1- ions. As a chemical equilibrium reaction, the equilibrium constant, known as the ion product or the product of the equilibrium concentration of the two ion species, has been extensively measured by chemists over the liquid water temper-ature and pressure range. The experimental data have been nonlinear least-squares fitted to chemical thermodynamic-based equilibrium equations, which have been accepted as the industrial standard for 35 years. In this study, a new and statistical-physics-based water ion product equation is presented, in which, the ions are the positively charged protons and the negatively charged proton-holes or prohols. Nonlinear least squares fits of our equation to the experimental data in the 0-100 ℃ pure liquid water range, give a factor of two better precision than the 35-year industrial standard.     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.