Some approximate solutions of dynamic problems in the linear theory of thin elastic shells

Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.

On separating propagating and non-propagating dynamics in fluid-flow equations

The ability to separate acoustically radiating and non-radiating components in fluid flow is desirable to identify the true sources of aerodynamic sound, which can be expressed in terms of the non-radiating flow dynamics. These non-radiating components are obtained by filtering the flow field. Two linear filtering strategies are investigated: one is based on a differential operator, the other employs convolution operations. Convolution filters are found to be superior at separating radiating and non-radiating components. Their ability to decompose the flow into non-radiating and radiating components is demonstrated on two different flows: one satisfying the linearized Euler and the other the Navier-Stokes equations. In the latter case, the corresponding sound sources are computed. These sources provide good insight into the sound generation process. For source localization, they are found to be superior to the commonly used sound sources computed using the steady part of the flow. Copyright © 2009 by S. Sinayoko, A. Agarwal, Z. Hu.

Electrolyte electroreflectance spectroscopy studies on the interfacial behavior of the near-surface In0.15Ga0.85As/GaAs quantum well electrode vertical bar non-aqueous electrolyte

Electrolyte electroreflectance spectra of the near-surface strained-layer In0.15Ga0.85As/GaAs double single-quantum-well electrode have been studied at different biases in non-aqueous solutions of ferrocene and acetylferrocene. The optical transitions, the Franz-Keldysh oscillations (FKOs) and the quantum confined Stark effects (QCSE) of In0.15Ga0.85As/GaAs quantum well electrodes are analyzed. Electric field strengths at the In0.15Ga0.85As/GaAs interface are calculated in both solutions by a fast Fourier transform analysis of FKOs. A dip is exhibited in the electric field strength versus bias (from 0 to 1.2 V) curve in ferrocene solution. A model concerning the interfacial tunneling transfer of electrons is used to explain the behavior of the electric field. (C) 2001 Elsevier Science B.V. All rights reserved.

The Category-Theoretic Solution of Recursive Domain Equations

Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories. To apply these general ideas we introduce Wand's ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott's universal domain method can be included too.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

New vortex solutions of Jackiw-Pi model

Based on current phi-mapping topological theory, a kind of self-dual equations in Jackiw-Pi model are studied. We first obtain explicit, self-dual solutions that satisfy Liouville equation which contains delta-function. Then we get perfect vortex solutions which reflect the system's internal topological structure, and consequently the quantization of flux.

Seeing 'Ghost' Solutions in Stereo Vision

A unique matching is a stated objective of most computational theories of stereo vision. This report describes situations where humans perceive a small number of surfaces carried by non-unique matching of random dot patterns, although a unique solution exists and is observed unambiguously in the perception of isolated features. We find both cases where non-unique matchings compete and suppress each other and cases where they are all perceived as transparent surfaces. The circumstances under which each behavior occurs are discussed and a possible explanation is sketched. It appears that matching reduces many false targets to a few, but may still yield multiple solutions in some cases through a (possibly different) process of surface interpolation.

Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

Aqueous solutions of HEC and hmHEC: effects of molecular mass versus hydrophobic associations on hydrodynamic and thermodynamic parameters.

Aqueous solutions of amphiphilic polymers usually comprise of inter- and intramolecular associations of hydrophobic groups often leading to a formation of a rheologically significant reversible network at low concentrations that can be identified using techniques such as static light scattering and rheometry. However, in most studies published till date comparing water soluble polymers with their respective amphiphilic derivatives, it has been very difficult to distinguish between the effects of molecular mass versus hydrophobic associations on hydrodynamic (intrinsic viscosity [g]) and thermodynamic parameters (second virial coefficient A2), owing to the differences between their degrees of polymerization. This study focuses on the dilute and semi-dilute solutions of hydroxyethyl cellulose (HEC) and its amphiphilic derivatives (hmHEC) of the same molecular mass, along with other samples having a different molecular mass using capillary viscometry, rheometry and static light scattering. The weight average molecular masses (MW) and their distributions for the nonassociative HEC were determined using size exclusion chromatography. Various empirical approaches developed by past authors to determine [g] from dilute solution viscometry data have been discussed. hmHEC with a sufficiently high degree of hydrophobic modification was found to be forming a rheologically significant network in dilute solutions at very low concentrations as opposed to the hmHEC with a much lower degree of hydrophobic modification which also enveloped the hydrophobic groups inside the supramolecular cluster as shown by their [g] and A2. The ratio A2MW/[g], which takes into account hydrodynamic as well as thermodynamic parameters, was observed to be less for associative polymers compared to that of the non-associative polymers.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Liquid-liquid miscibility and volumetric properties of aqueous solutions of ionic liquids as a function of temperature

The volumetric properties of seven {water + ionic liquid} binary mixtures have been studied as a function of temperature from (293 to 343) K. The phase behaviour of the systems was first investigated using a nephelometric method and excess molar volumes were calculated from densities measured using an Anton Paar densimeter and fitted using a Redlich-Kister type equation. Two ionic liquids fully miscible with water (1-butyl-3-methylimidazolium tetrafluoroborate ([CCIm][BF]) and 1-ethyl-3-methylimidazolium ethylsulfate ([CCIm][EtSO])) and five ionic liquids only partially miscible with water (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([CCIm][NTf]), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([CCIm][NTf]), 1-butyl-3-methylimidazolium hexafluorophosphate ([CCIm][PF]), 1-butyl-3-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide ([CCPyrro][NTf]), and butyltrimethylammonium bis(trifluoromethylsulfonyl)imide ([N][NTf])) were chosen. Small excess volumes (less than 0.5 cm · mol at 298 K) are obtained compared with the molar volumes of the pure components (less than 0.3% of the molar volume of the pure ionic liquid). For all the considered systems, except for {[CCIm][EtSO] + water}, positive excess molar volumes were calculated. Finally, an increase of the non-ideality character is observed for all the systems as temperature increases. © 2009 Elsevier Ltd. All rights reserved.

Molecular basis of non-mutational derepression of ramA in Klebsiella pneumoniae

Objectives: The ram locus, consisting of the romA–ramA genes, is repressed by the tetracycline-type regulator RamR, where regulation is abolished due to loss-of-function mutations within the protein or ligand interactions. The aim of this study was to determine whether the phenothiazines (chlorpromazine and thioridazine) directly interact with RamR to derepress ramA expression.

Methods: Quantitative real-time PCR analyses were performed to determine expression levels of the romA–ramA genes after exposure to the phenothiazines. Electrophoretic mobility shift assays (EMSAs) and in vitro transcription experiments were performed to show direct binding to and repression by RamR. Direct binding of the RamR protein to the phenothiazines was measured by fluorescence spectroscopy experiments and molecular docking models were generated using the RamR crystal structure.

Results: Exposure to either chlorpromazine or thioridazine resulted in the up-regulation of the romA–ramA genes. EMSAs and in vitro transcription experiments demonstrated that both agents reduce/abolish binding and enhance transcription of the target PI promoter upstream of the ramR–romA genes in Klebsiella pneumoniae compared with RamR alone. Fluorescence spectroscopy measurements demonstrated that RamR directly binds both chlorpromazine and thioridazine with micromolar affinity. Molecular docking analyses using the RamR crystal structure demonstrated that the phenothiazines interact with RamR protein through contacts described for other ligands, in addition to forming unique strong polar interactions at positions D152 and K63.

Conclusions: These data demonstrate that phenothiazines can modulate loci linked to the microbe–drug response where RamR is an intracellular target for the phenothiazines, thus resulting in a transient non-mutational derepression of ramA concentrations.