On the regularity of the pressure field of relaxed solutions to Euler equations with variable density

In this paper we improve the regularity in time of the gradient of the pressure field in the solution of relaxed version of variational formulation proposed by V. I. Arnold and by Y. Brenier, for the incompressible Euler equations with variable density. We obtain that the pressure field is not only a measure, but a function in Lloc2((0,T);BVloc(D)) as an extension of the work of Ambrosio and Figalli (2008) in [1] to the variable density case. © 2013 Elsevier Ltd.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Jetting behaviour of polymer solutions in drop-on-demand inkjet printing

The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitative model is presented which predicts three different regimes of behaviour depending upon the jet Weissenberg number Wi and extensibility of the polymer molecules. In regime I (Wi < ½) the polymer chains are relaxed and the fluid behaves in a Newtonian manner. In regime II (½ < Wi < L) where L is the extensibility of the polymer chain the fluid is viscoelastic, but the polymer do not reach their extensibility limit. In regime III (Wi > L) the chains remain fully extended in the thinning ligament. The maximum polymer concentration at which a jet of a certain speed can be formed scales with molecular weight to the power of (1-3ν), (1-6ν) and -2ν in the three regimes respectively, where ν is the solvent quality coefficient. Experimental data obtained with solutions of mono-disperse polystyrene in diethyl phthalate with molecular weights between 24 - 488 kDa, previous numerical simulations of this system, and previously published data for this and another linear polymer in a variety of “good” solvents, all show good agreement with the scaling predictions of the model.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Solutions for the flow of a micropolar fluid in a porous channel

How various additives can increase some cardio-vascular diseases and effects of transport for albumin and glucose through permeable membranes are some important studies in biomechanics. The rolling phenomena of the leucocytes gives rise to an inflammatory reaction along a vascular wall. Initiated by Eringen [5], a micropolar fluid is a satisfactory model for flows of fluids which contain micro-constituents which can undergo rotation.

Re-Lifing commercial buildings : design and construction solutions for existing buildings

The resources listed in this document describe the design and construction opportunities available to building owners who wish to re-Life their properties. They do not yet examine management opportunities, which may also help owners improve the efficiency of their existing stock.

Adopting BIM for Facilities Adopting BIM for Facilities Management : Solutions for Managing the Sydney Opera House

The digital modelling research stream of the Sydney Opera House FM Exemplar Project has demonstrated significant benefits in digitising design documentation and operational and maintenance manuals. Since Sydney Opera House did not have digital models of its structure, there was an opportunity to investigate the application of digital modelling using standardised Building Information Models (BIM) to support facilities management (FM).The focus of this investigation was on the following areas:the re-usability of standardised BIM for FM purposesthe potential of BIM as an information framework acting as integrator for various FM data sources the extendibility and flexibility of the BIM to cope with business-specific data and requirements commercial FM software using standardised BIMthe ability to add (organisation-specific) intelligence to the modela roadmap for Sydney Opera House to adopt BIM for FM.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.