Weierstrass Points and Regular Maps

It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map.     

Surface-enhanced Raman scattering study of polymer on metals. III. Chemisorbed polybenzimidazole and its corrosion-inhibiting properties at high temperature

Chemisorption of polybenzimidazole on silver and copper etched with nitric acid has been observed by surface-enhanced Raman scattering (SERS). The polymer is found to react chemically with silver, forming a complexed film on the surface. The SERS spectra show that polybenzimidazole film inhibits oxidation of the metal at high temperature, unlike chemisorbed benzimidazole, benzotriazole, and poly(4-vinyl pyridine). © 1992 John Wiley & Sons, Inc.     

A generalized Adadorov theory for anisotropic thin-walled beams

This paper presents a generalized Adadorov theory for anisotropic thin—walled beams. The theory takes account of the shear strain of the middle surface, which exerts a significant influence on the anisotropic thin-walled beams. A new approach is established to solve the governing equations, which have the same form for both open and closed section beams. The numerical examples show that the effects of the shear strain cannot be neglected for this class of beams.This work was part of research project supported by the National Natural Science Foundation of China     

Molecular modeling study on surface,thermal, mechanical and gas diffusion properties of chitosan

The motivation of this work is to provide reliable and accurate modeling studies of the physical (surface, thermal, mechanical and gas diffusion) properties of chitosan (CS) polymer. Our computational efforts have been devoted to make a comparison of the structural bulk properties of CS with similar type of polymers such as chitin and cellulose through cohesive energy density, solubility parameter, hydrogen bonding, and free volume distribution calculations. Atomistic modeling on CS polymer using molecular mechanics (MM) and molecular dynamics (MD) simulations has been carried out in three dimensionally periodic and effective two dimensionally periodic condensed phases. From the equilibrated structures, surface energies were computed. The equilibrium structure of the films shows an interior region of mass density close to the value in the bulk state. Various components of energetic interactions have been examined in detail to acquire a better insight into the interactions between bulk structure and the film surface. MD simulation (NPT ensemble) has also been used to obtain polymer specific volume as a function of temperature. It is demonstrated that these V–T curves can be used to locate the volumetric glass transition temperature (T_g) reliably. The mechanical properties of CS have been obtained using the strain deformation method. Diffusion coefficients of O₂, N₂, and CO₂ gas molecules at 300 K in CS have been estimated. The calculated properties of CS are comparable with the experimental values reported in the literature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1260–1270, 2007     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A partial differential equation which describes an interatomic surface

In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.