Chaotic advection in compressible helical flow

Compressible helical flow with div v not equal to 0 drastically increases the area of chaotic dynamics and mixing properties when the helicity parameter is spatially dependent. We show that the density dependence on the z coordinate can be incorporated in new variables in a way that leads to a Hamiltonian formulation of the system. This permits the application of various important results like the Kolmogorov-Arnold-Moser theory and, particularly, an understanding of why and in which sense the compressible helical flow is "more chaotic" than the incompressible one. Simulation demonstrates this property for an analog of the ABC flow. An interesting type of the dynamical system with "dense" island chains is described.     

Steady vortex structures in inviscid flows in channels

The problem of inviscid incompressible flow through a rectangular channel is considered under the normal velocity component given at the chanel boundaries and the fluid vorticity at the entry. Nonconventional steady flows with recirculation zones and different functional dependences of the vorticity on the stream function are found by analytical and numerical methods. The stability of the steady regimes obtained is analyzed using the numerical solution of the time-dependent problem by the particle-in-cells method.     

Scenarios of the onset of unsteady regimes in the problem of plane convective flow through a porous medium

The problem of plane convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. The onset of unsteady regimes is investigated numerically. It is shown that their onset scenarios depend on the vessel dimensions and the seepage Rayleigh number and may be as follows: the generation of stable and unstable periodic regimes as a result of a one-sided bifurcation, the generation of a stable periodic regime as a result of an Andronov-Hopf cosymmetric bifurcation, the formation of a chaotic attractor, the branching-out of a stable quasi-periodic regime from a point of a single-parameter family of steady-state regimes, and the generation of unstable periodic regimes as a result of disintegration of homoclinic trajectories. The specifics of most of the bifurcations mentioned above are attributable to the cosymmetry of the problem considered.     

On the choice of a method for integrating the equations of motion of a set of fluid particles

Results of numerical experiments are described in which the evolution of a set of fluid particles is computed using various time integration methods. Known exact solutions of the inviscid equations are used to analyze the errors of the methods occurring on various time intervals at the same computational costs. An adaptive algorithm for choosing an integration method depending on the domain of the phase space is proposed. The numerical results are presented as tables and plots.     

Quantifying uncertainty in the measurement of arsenic in suspended particulate matter by Atomic Absorption Spectrometry with hydride generator

Arsenic is the toxic element, which creates several problems in human being specially when inhaled through air. So the accurate and precise measurement of arsenic in suspended particulate matter (SPM) is of prime importance as it gives information about the level of toxicity in the environment, and preventive measures could be taken in the effective areas. Quality assurance is equally important in the measurement of arsenic in SPM samples before making any decision. The quality and reliability of the data of such volatile elements depends upon the measurement of uncertainty of each step involved from sampling to analysis. The analytical results quantifying uncertainty gives a measure of the confidence level of the concerned laboratory. So the main objective of this study was to determine arsenic content in SPM samples with uncertainty budget and to find out various potential sources of uncertainty, which affects the results. Keeping these facts, we have selected seven diverse sites of Delhi (National Capital of India) for quantification of arsenic content in SPM samples with uncertainty budget following sampling by HVS to analysis by Atomic Absorption Spectrometer-Hydride Generator (AAS-HG). In the measurement of arsenic in SPM samples so many steps are involved from sampling to final result and we have considered various potential sources of uncertainties. The calculation of uncertainty is based on ISO/IEC17025: 2005 document and EURACHEM guideline. It has been found that the final results mostly depend on the uncertainty in measurement mainly due to repeatability, final volume prepared for analysis, weighing balance and sampling by HVS. After the analysis of data of seven diverse sites of Delhi, it has been concluded that during the period from 31^st Jan. 2008 to 7^th Feb. 2008 the arsenic concentration varies from 1.44 ± 0.25 to 5.58 ± 0.55 ng/m³ with 95% confidence level (k = 2).     

Emergence of Self-Excited Oscillations in Flows of Inviscid Fluids in a Channel

Computational Mathematics and Mathematical Physics - The mechanism of self-excited oscillations arising in an ideal incompressible fluid flowing through a rectangular channel is studied...     

Numerical Investigation of the Second Transition in the Problem of Plane Convective Flow through a Porous Medium

The problem of convective flow through a porous medium in a plane rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. Single-parameter families of steady-state regimes resulting from the existence of cosymmetry of the corresponding differential equations are investigated using the Galerkin method. The onset and development of instability on these families and the characteristics of convective regimes as functions of the seepage Rayleigh number and the rectangle side ratio are studied. It is shown that the number of regimes which lose stability, the instability type, the number of convective rollers developed, and the heat transfer depend significantly on the vessel geometry. Several bifurcations of single-parameter families of steady-state regimes are identified and investigated.     

Structural characteristics of different types of nanoparticles synthesised in mesomorphic metal alkanoates

The class of thermotropic ionic liquid crystals (LCs) of the metal alkanoates possesses a number of unique properties, such as intrinsic ionic conductivity, high dissolving ability and ability to form time-stable mesomorphic glasses. These ionic LCs can be used as nanoreactors for the synthesis and stabilisation of different types of nanoparticles (NPs). Thus, some semiconductors, metals and core/shell NPs were chemically synthesised in the thermotropic ionic liquid crystalline phase (smectic A) of the cadmium octanoate (CdC₈) and of the cobalt octanoate (CoC₈). By applying the scanning electron microscopy, the cadmium and cobalt octanoate composites containing CdS, Au, Ag and core/shell Au/CdS NPs have been studied. NPs’ sizes and dispersion distribution of the NPs’ size in the nanocomposites have been obtained.     

Numerical study of an inviscid incompressible flow through a channel of finite length

A two‐dimensional inviscid incompressible flow in a rectilinear channel of finite length is studied numerically. Both the normal velocity and the vorticity are given at the inlet, and only the normal velocity is specified at the outlet. The flow is described in terms of the stream function and vorticity. To solve the unsteady problem numerically, we propose a version of the vortex particle method. The vorticity field is approximated using its values at a set of fluid particles. A pseudo‐symplectic integrator is employed to solve the system of ordinary differential equations governing the motion of fluid particles. The stream function is computed using the Galerkin method. Unsteady flows developing from an initial perturbation in the form of an elliptical patch of vorticity are calculated for various values of the volume flux of fluid through the channel. It is shown that if the flux of fluid is large, the initial vortex patch is washed out of the channel, and when the flux is reduced, the initial perturbation evolves to a steady flow with stagnation regions. Copyright © 2008 John Wiley & Sons, Ltd.