A periodic functional approach to the calculus of variations and the problem of time-dependent damped harmonic oscillators

I discuss the problem of time-dependent harmonic oscillators on the basis of a periodic functional approach to the calculus of variations. Both the Lagrangian and Hamiltonian formulations are explored and discussed in some detail. Some interesting consequences are revealed.     

The influence of flow acceleration on tidal stream turbine wake dynamics: A numerical study using a coupled BEM–CFD model

Studies of tidal stream turbine performance and of wake development are often conducted in tow-tanks or in regulated flumes with uniform flows across the turbine. Whilst such studies can be very useful, it is questionable as to what extent the results would differ if the flows were more complex in nature, for instance if the flows were unsteady or non-uniform or even both. This study aims to explore whether the results would be affected once we move away from the uniform flow scenario. A numerical modelling study is presented in which tidal stream turbine performance and wake development in non-uniform flow conditions are assessed. The model implements the Blade Element Momentum method for characterising turbine rotor source terms which are used within a computational fluid dynamics model for predicting the interaction between the turbines and the surrounding flow. The model is applied to a rectangular domain and a range of slopes are implemented for the water surface to instigate an increase in flow velocity along the domain. Within an accelerated flow domain wake recovery occurred more rapidly although rotor performance was not affected.     

Inter-comparison and validation of computational fluid dynamics codes in two-stage meandering channel flows

This paper presents a study in the inter-comparison and validation of three-dimensional computational fluid dynamics codes which are currently used in river engineering. Finite volume codes PHOENICS, FLUENT and SSIIM; and finite element code TELEMAC3D are considered in this study. The work has been carried out by competent hydraulic modellers who are users of the codes and not involved in their development. This paper is therefore written from the perspective of independent practitioners of the techniques. In all codes, the flow calculations are performed by solving the three-dimensional continuity and Reynolds-averaged Navier–Stokes equations with the k–ε turbulence model. The application of each code was carried out independently and this led to slightly different, but nonetheless valid, models. This is particularly seen in the different boundary conditions which have been applied and which arise in part from differences in the modelling approaches and methodology adopted by the different research groups and in part from the different assumptions and formulations implemented in the different codes. Similar finite volume meshes are used in the simulations with PHOENICS, FLUENT and SSIIM while in TELEMAC3D, a triangular finite element mesh is used. The ASME Journal of Fluids Engineering editorial policy is taken as a minimum framework for the control of numerical accuracy. In all cases, grid convergence is demonstrated and conventional criteria, such as Y⁺, are satisfied. A rigorous inter-comparison of the codes is performed using large-scale experimental data from the UK Flood Channel Facility for a two-stage meandering channel. This example data set shows complex hydraulic behaviour without the additional complications found in natural rivers. Standardised methods are used to compare each model with the available experimental data. Results are shown for the streamwise and transverse velocities, secondary flow, turbulent kinetic energy, bed shear stress and free surface elevation. They demonstrate that the models produce similar results overall, although there are some differences in the predicted flow field and greater differences in turbulent kinetic energy and bed shear stress. This study is seen as an essential first step in the inter-comparison of some of the computational fluid dynamics codes used in the field of river engineering.     

Effect of Silica Particle Size on Polymer Adsorption. Morphological,Energetic and Conformational Relationships

A series of six chemically treated and untreated fumed silicas with increasing particle size (ranging from the nano- to the micrometer size) was prepared. Surface areas (and morphologies) and surface energies were determined by nitrogen adsorption and inverse gas chromatography, respectively. The adsorption of a series of PDMS with different and well-defined molecular weights was studied at different polymer concentrations. Amounts of adsorbed polymer were determined by gravimetry and the energies of adsorption were assessed by flow-microcalorimetry. Results are discussed in terms of particle surface energy and morphology effects on the conformation and the inter-connectivity of adsorbed polymer molecules.     

Solution structure of papain as studied by molecular mechanics and molecular dynamics techniques

In this paper, we report the molecular mechanics and molecular dynamics studies of the hydration of papain using the AMBER and CHARMm programs. We studied papain in an environment with minimal hydration involving only the X-ray waters and also in the hydrated environment by adding an extra 9 Å layer of water around the residues. The effect of nonbond cutoff was studied by performing minimizations with 8 Å and 15 Å nonbond cutoffs using the program AMBER. Two different solvent models—a constant dielectric and a distance-dependent dielectric—were considered. The AMBER-minimized structure and the average structure obtained from the CHARMm simulations for papain solvated with X-ray waters are presented and compared with the X-ray crystal structure results. Results of a similar comparison of the hydrated structures were also presented. The calculated root mean square deviation between the minimized structure and the X-ray structure is smaller for the hydrated system than for the system hydrated with only the X-ray waters. Results of the molecular mechanics and molecular dynamics simulations were presented for the various regions of papain. The hydration of the active site of papain and the effect of hydration on the torsional motion of the active site residues are presented. © 1996 by John Wiley & Sons, Inc.     

Numerical approximations and Padé approximants for a fractional population growth model

This paper presents an efficient numerical algorithm for approximate solutions of a fractional population growth model in a closed system. The time-fractional derivative is considered in the Caputo sense. The algorithm is based on Adomian’s decomposition approach and the solutions are calculated in the form of a convergent series with easily computable components. Then the Padé approximants are effectively used in the analysis to capture the essential behavior of the population u(t) of identical individuals.     

Spectral time moment analysis of microgel structure and dynamics

The structure and dynamics of crosslinked nanoparticles (microgels) made out of hydroxypropylcellulose (HPC) polymer chains were studied using dynamic light scattering spectroscopy. The microgel light scattering spectra were found to be highly nonexponential requiring a spectral time moment analysis in which the spectra were fit to a sum of stretched exponentials. Each term offers three parameters for analysis and represents a single spectral mode. At room temperature microgel spectra reveal three modes. Two faster modes are almost diffusive and correspond to apparent sizes of 25 and 450–650 nm. The slowest mode is independent of scattering angle and is reminiscent of the slow polymer mode observed in identical non‐crosslinked polymer solutions. When solution temperature is varied from 23 to 45°C and back, the microgel undergoes a reversible volume phase transition between 40 and 45°C. According to the time‐moment analysis, above the transition temperature two faster modes collapse into one with apparent hydrodynamic radius of 100–150 nm, while the slow mode remains largely unchanged. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 771–781, 2008     

Improved image contrast with mangafodipir trisodium (MnDPDP) during MR-guided percutaneous cryosurgery of the liver

The present study was undertaken to measure the gain observed in the liver-to-tumor contrast of perioperative images when using mangafodipir trisodium, a liver-specific contrast agent, during percutaneous cryosurgery of the liver performed under the guidance of magnetic resonance images. Retrospective quantitative analyses of MR images were performed on eleven patients having a total of 30 liver tumors treated by MR-guided percutaneous cryosurgery. An initial group of four patients were treated with no contrast agent, and was compared with a second group of 7 patients who received an intravenous injection of 5 microM/kg of mangafodipir for their cryosurgery. The percutaneous cryosurgery was monitored under the near-real-time-imaging mode of a 0.5T open-configuration MRI system using a T(1)-weighted Gradient-recalled echo pulse sequence. A significant improvement in the liver-to-tumor contrast-to-noise ratio was observed with mangafodipir (p < 0.05, paired t test) in 0.5T preoperative images. Along with the stability of the mangafodipir contrast enhancement during the entire cryosurgical procedure, the resulting gain in contrast allowed for better visualizing the presence of residual untreated tumor margins at the periphery of the cryosurgery iceball directly from perioperative images acquired with patients under narcosis. Consequently, it not only became easier for the interventionalist to determine the need for an additional cryoprobe to increase the size of the iceball during the procedure, but also to decide on the appropriate end point of the cryosurgery.     

Polymeric reagent synthesis of luteinizing hormone-releasing hormone

Luteinizing hormone-releasing hormone, pGlu-His-Trp-Ser-Tyr-Gly-Leu-Arg-Pro-Gly-NH₂,² was synthesized in a stepwise manner by two approaches: the use of insoluble polymeric active esters derived from (4-hydroxy-3-nitro)benzylated polystyrene and that of solubleN,N-dicyclohexylcarbodiimide. The overall yields of the syntheses were 40 and 7%, respectively. The efficiencies of the two synthetic routes, in which identical intermediate peptides were prepared, are compared.