Boundary control of the generalized Korteweg–de Vries–Burgers equation

This paper considers the boundary control problem of the generalized Korteweg–de Vries–Burgers (GKdVB) equation on the interval [0, 1]. We derive a control law of the form and α is a positive integer, and prove that it guarantees L ²-global exponential stability, H ¹-global asymptotic stability, and H ¹-semiglobal exponential stability. Numerical results supporting the analytical ones for both the controlled and uncontrolled equations are presented using a finite element method.     

Thrust performance of unsteady propulsors using a novel measurement system,and corresponding wake patterns

An apparatus is described for the measurement of unsteady thrust and propulsive efficiency produced by biologically inspired oscillating hydrodynamic propulsors. Force measurement is achieved using a strain-gauge-based force transducer, augmented with a lever to amplify or attenuate the applied force and control the measurement sensitivity and natural frequency of vibration. The lever can be used to tune the system to a specific application and it is shown that, using the lever, the stiffness can be made to increase more rapidly than the measurement sensitivity decreases. Efficiency is computed from measurements of the time-averaged power imparted to the fluid. The apparatus is applied to two different propulsors, demonstrating the versatility of the system; wake visualizations are examined, which provide insight into the physical mechanisms of efficient propulsion.

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Investigation of heat transfer by means of pool film boiling on vertical cylinders in gravity

In this study, the heat transfer by means of pool film boiling on immersed vertical cylindrical rods was investigated. For this purpose, the rods with various dimensions, which have been heated up to 600°C, were immersed in a pure water pool in the different temperatures. The centre temperature and water temperature versus operation time were measured by K type thermocouples at the atmospheric pressure. After experimental studies, the surface temperatures of rods and heat transfer coefficients were calculated by means of Lumped method from the measured temperatures. Consequently, an empirical equation was developed between the Nusselt, Grashof, Prandtl and Jakob numbers. The experimental results showed that the specimens having the same characteristic lengths exhibited the same heat transfers performance although the specimen’s diameters and lengths differed considerably.     

Nonparabolic Asymptotic Limits of Solutions of the Heat Equation on $${\mathbb{R}}^N$$

In this paper, we construct solutions u(t,x) of the heat equation on such that has nontrivial limit points in as t → ∞ for certain values of μ > 0 and β > 1/2. We also show the existence of solutions of this type for nonlinear heat equations.      

An investigation of the stability in the large for an autonomous second-order two-degree-of-freedom system

An extension to an algorithm due to Simpson has been developed for the analysis of a second-order two-degree-of-freedom autonomous system. The form of equations considered arises from the study of mechanical systems with a single concentrated non-linearity and the method assumes a solution made up of harmonic terms whose amplitudes vary slowly in time. For a system possessing a stable equilibrium point and an unstable limit cycle arising from a subcritical Hopf bifurcation, the method has been applied to the problem of predicting the basin of attraction of the equilibrium point. The method reduces the problem from a search in four-dimensional phase space to a search for a boundary in a plane defined by amplitudes a₁ and a₂ in the assumed form of the solution. The method was applied to four weakly non-linear systems in which the non-linearity was due to either a linear spring with a small amount of cubic hardening or a linear spring with freeplay. Agreement was shown to be good in the cases considered. However, it would be expected that the method would not give such accurate results if the non-linear effect was more significant. This was illustrated for the case of the cubic hardening non-linearity.     

Constitutive framework optimized for myocardium and other high-strain, laminar materials with one fiber family

Central to this analysis is the identification of six rotation invariant scalars α_1-6 that succinctly define the strain in materials that have one family of parallel fibers arranged in laminae. These scalars were chosen so as to minimize covariance amongst the response terms in the hyperelastic limit, and they are termed strain attributes because it is necessary to distinguish them from strain invariants. The Cauchy stress t is expressed as the sum of six response terms, almost all of which are mutually orthogonal for finite strain (i.e. 14 of the 15 inner products vanish). For small deformations, the response terms are entirely orthogonal (i.e. all 15 inner products vanish). A response term is the product of a response function with its associated kinematic tensor. Each response function is a scalar partial derivative of the strain energy W with respect to a strain attribute. Applications for this theory presently include myocardium (heart muscle) which is often modeled as having muscle fibers arranged in sheets. Utility for experimental identification of strain energy functions is demonstrated by showing that common tests on incompressible materials can directly determine terms in W. Since the described set of strain attributes reduces the covariance amongst response terms, this approach may enhance the speed and precision of inverse finite element methods.     

Effect of variable ambient temperature on fin efficiency in a two-dimensional flow passage

The fin efficiency in a heat exchanger element that is a simplification of one row in a tube-and-fin heat exchanger was theoretically examined within wide ranges of the affecting variables: the conventional fin efficiency and the isothermal effectiveness of the heat exchanger. These variables are suggested for use also in the further studies. An analytical solution can be found for the case of a constant heat transfer coefficient. The ambient temperature variation alone decreases the fin efficiency less than 4%. The local heat transfer coefficient obtained from the numerical fluid flow simulations is strongly affected by the fin properties because the thermal boundary conditions for the fluid flow changes. On a poorly conducting fin surface the heat transfer coefficient in front of the fin base is much larger than on an isothermal fin because the heat flux is increasing in the flow direction. At low fin efficiencies this compensates for the decrease in fin efficiency due to ambient temperature variation.     

Degenerate Conformally Invariant Fully Nonlinear Elliptic Equations

We establish Liouville theorems for , entire solutions and locally Lipschitz entire weak solutions to general degenerate conformally invariant fully nonlinear elliptic equations of second order. For applications to local gradient estimates of solutions of general conformally invariant fully nonlinear elliptic equations of second order, see [20].     

Stress relaxation of large amplitudes and long timescales in soft thermoplastic and filled elastomers

We propose a model for describing mesoscale relaxation mechanisms in soft thermoplastic elastomers and also in the high-temperature regime of filled rubbers. The model consists of hard spheres embedded in an elastic matrix. It is solved by dissipative particle dynamics. We study the response of the model to deformations of various amplitudes. We show that it displays slow relaxation processes of large amplitudes that are related to irreversible reorganizations at a mesoscopic scale. We characterize these reorganizations as buckling of instabilities that change the local environment of the hard inclusions. Paper presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Modelling Turbulent Premixed Combustion Using the Level Set Approach for Reynolds Averaged Models

A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described in terms of the G-equation. The numerical instabilities of the G-field are resolved using a reinitialisation procedure. For the G-points near the flame surface an algorithm proposed by Russo and Smereka [1] and modificated by Düsing [2] is presented. For all other points the standard Sussman algorithm is employed. Fluid properties are conditioned on the flame front position using a burnt-unburnt probability function across the flame front. Computations are performed using the code FASTEST-3D [3] which is a flow solver for a non-orthogonal, block-structured grid. The computational examples include two test cases, the first containing the propagation of two circular merging flames and the second one containing the simulation of the ORACLES-burner [4].