The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier–Stokes–Duhem equations ...together with the continuity and thermal conduction equation. The novel approach reported here adopts instead, a discontinuous Lagrangian approach, i.e. from Hamilton’s principle together with a discontinuous Lagrangian for the case of a general viscous flow. It is shown that ensemble averaging of the equation of motion resulting from the Euler–Lagrange equations, under the assumption of irrotational flow, leads to a weakly nonlinear wave equation for the velocity potential: in effect a generalisation of Kuznetsov’s well known equation with an additional term due to thermodynamic non-equilibrium effects.
•Viscous flow with thermal conduction is deducible from a discontinuous Lagrangian.•Non-classical effects occur beyond thermodynamic equilibrium.•By ensemble averaging a non-classical equation of motion is derived.•In the irrotational and weakly nonlinear case a generalised Kuznetsov equation is obtained.
The discontinuous Lagrangian approach, allowing for a variational description of irreversible phenomena in continuum theory such as viscosity and thermal conductivity, is utilised for the analysis of ...damped acoustic waves. Starting from a Lagrangian for general viscous flow theory, by linearisation of the resulting Euler–Lagrange equations and performing an ensemble average, a single wave equation for the density perturbations is obtained, being the one resulting from classical Navier–Stokes theory with an additional term due to thermodynamic non-equilibrium. By considering harmonic waves, the respective non-classical dispersion relation and its implications are analysed.
•Viscous flow with thermal conduction is deducible from a discontinuous Lagrangian.•Non-classical effects occur beyond thermodynamic equilibrium.•By linearisation and ensemble averaging a non-classical wave equation is derived.•The corresponding dispersion relation contains non-equilibrium terms.
In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the ...description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented.
•A generalized Clebsch transformation is established applying to viscous flow.•The resulting 5 equations are a first integral of Navier–Stokes-equations.•An axisymmetric stagnation flow against a solid wall is considered as flow example.•Perspectives of the method for other problems, e.g. in solid mechanics are discussed.
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the ...resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.
A recently proposed variational principle with a discontinuous Lagrangian for viscous flow is reinterpreted against the background of stochastic variational descriptions of dissipative systems, ...underpinning its physical basis from a different viewpoint. It is shown that additional non-classical contributions to the friction force occurring in the momentum balance vanish by time averaging. Accordingly, the discontinuous Lagrangian can alternatively be understood from the standpoint of an analogous deterministic model for irreversible processes of stochastic character. A comparison is made with established stochastic variational descriptions and an alternative deterministic approach based on a first integral of Navier-Stokes equations is undertaken. The applicability of the discontinuous Lagrangian approach for different Reynolds number regimes is discussed considering the Kolmogorov time scale. A generalization for compressible flow is elaborated and its use demonstrated for damped sound waves.
Abstract Aim To conduct a meta-analysis evaluating the effect of pharmacist intervention on glycemic control. Methods A systematic search of Medline and CENTRAL was conducted from the earliest ...possible date through June 2010. Trials were included if they were randomized controlled trials in a diabetic population, evaluated any form of pharmacist intervention and reported data on hemoglobin A1C (A1C). A random-effects model was used to calculate weighted mean differences (WMDs) and 95% confidence intervals. Results Fourteen trials ( n = 2073) evaluating the effect of pharmacist intervention on glycemic control were identified. Pharmacist intervention significantly lowered A1C ( n = 14 trials, WMD −0.76%, 95%CI −1.06 to −0.47) and fasting blood glucose (FBG) ( n = 4 trials, WMD −29.32 mg/dL, 95%CI −39.54 to −19.10). A moderate to high degree of statistical heterogeneity was observed in these analyses ( I2 ≥ 44.1% for both). Conclusions Our findings demonstrate statistically and clinically significant associations between pharmacist intervention and improvement in glycemic control.
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