The intertwining lifting theorem for ordered groups

Sz.-Nagy's dilation theorem for a contraction on a Hilbert space has been extended by Mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group. We generalize to this case the intertwining lifting theorem of Sz.-Nagy and Foias. Some previous interpolation results on ordered groups are obtained as consequences.     

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 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.     

The LEM exponential integrator for advection–diffusion–reaction equations

We implement a second-order exponential integrator for semidiscretized advection–diffusion–reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja–Euler–Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.     

Interpolation by a Game

We introduce a notion of a real game (a generalisation of the Karchmer-Wigderson game (cf. [3]) and of real communication complexity, and relate this complexity to the size of monotone real formulas and circuits. We give an exponential lower bound for tree-like monotone protocols (defined in [4, Definition 2.2]) of small real communication complexity solving the monotone communication complexity problem associated with the bipartite perfect matching problem. This work is motivated by a research in interpolation theorems for prepositional logic (by a problem posed in [5, Section 8], in particular). Our main objective is to extend the communication complexity approach of [4, 5] to a wider class of proof systems. In this direction we obtain an effective interpolation in a form of a protocol of small real communication complexity. Together with the above mentioned lower bound for tree-like protocols this yields as a corollary a lower bound on the number of steps for particular semantic derivations of Hall's theorem (these include tree-like cutting planes proofs for which an exponential lower bound was demonstrated in [2]).     

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.     

A hybrid finite-element–volume-of-fluid method for simulating free surface flows and interfaces

A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume-of-fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid-size-dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM-VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break-up of a capillary jet and the coalescence collision of two liquid drops.     

Reinforcement effect of MAA on nano‐CaCo3‐filled EPDM vulcanizates and possible mechanism

Methacrylic acid (MAA) was used as in situ surface modifier to improve the interface interaction between nano‐CaCO₃ particle and ethylene–propylene–diene monomer (EPDM) matrix, and hence the mechanical properties of nano‐CaCO₃‐filled EPDM vulcanizates. The results showed that the incorporation of MAA improved the filler–matrix interaction, which was proved by Fourier transformation infrared spectrometer (FTIR), Kraus equation, crosslink density determination, and scanning electron microscope (SEM). The formation of carboxylate and the participation of MAA in the crosslinking of EPDM indicated the strong filler–matrix interaction from the aspect of chemical reaction. The results of Kraus equation showed that the presence of MAA enhanced the reinforcement extent of nano‐CaCO₃ on EPDM vulcanizates. Crosslink density determination proved the formation of the ionic crosslinks in EPDM vulcanizates with the existence of MAA. The filler particles on tensile fracture were embedded in the matrix and could not be observed obviously, indicating that a strong interfacial interaction between the filler and the matrix had been achieved with the incorporation of MAA. Meanwhile, the presence of MAA remarkably increased the modulus and tensile strength of the vulcanizates, without negative effect on the high elongation at break. Furthermore, the ionic bond was thought to be formed only on filler surface because of the absolute deficiency of MAA, which resulted in the possible structure where filler particles were considered as crosslink points. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1226–1236, 2006