The cell mapping methods were originated by Hsu in 1980s for global analysis of nonlinear dynamical systems that can have multiple steady-state responses including equilibrium states, periodic motions, and chaotic attractors. The cell mapping methods have been applied to deterministic, stochastic, and fuzzy dynamical systems. Two important extensions of the cell mapping method have been developed to improve the accuracy of the solutions obtained in the cell state space: the interpolated cell mapping (ICM) and the set-oriented method with subdivision technique. For a long time, the cell mapping methods have been applied to dynamical systems with low dimension until now. With the advent of cheap dynamic memory and massively parallel computing technologies, such as the graphical processing units (GPUs), global analysis of moderate- to high-dimensional nonlinear dynamical systems becomes feasible. This paper presents a parallel cell mapping method for global analysis of nonlinear dynamical systems. The simple cell mapping (SCM) and generalized cell mapping (GCM) are implemented in a hybrid manner. The solution process starts with a coarse cell partition to obtain a covering set of the steady-state responses, followed by the subdivision technique to enhance the accuracy of the steady-state responses. When the cells are small enough, no further subdivision is necessary. We propose to treat the solutions obtained by the cell mapping method on a sufficiently fine grid as a database, which provides a basis for the ICM to generate the pointwise approximation of the solutions without additional numerical integrations of differential equations. A modified global analysis of nonlinear systems with transient states is developed by taking advantage of parallel computing without subdivision. To validate the parallelized cell mapping techniques and to demonstrate the effectiveness of the proposed method, a low-dimensional dynamical system governed by implicit mappings is first presented, followed by the global analysis of a three-dimensional plasma model and a six-dimensional Lorenz system. For the six-dimensional example, an error analysis of the ICM is conducted with the Hausdorff distance as a metric.

A simulator is designed to explore the interactive mechanism of a plasma jet with the liquid medium in the bulk-loaded liquid electrothermal chemical launching process. The properties of the plasma jet expanding in the liquid and the mixing characteristics of the plasma jet with liquid in the cylindrical chamber are studied using a high speed camera system. According to the experimental results, a two-dimensional axisymmetric unsteady compressible flow model has been proposed. The transient characteristics of the jet in flow field have been simulated. The results indicate that, during the expansion of the plasma jet in the liquid medium, there is relatively strong turbulent mixing. The interface between the two phases is not smooth and fluctuates with time stochastically. The higher the discharge voltage is, the stronger the Helmholtz instability effect will be. The Taylor cavity forming during the jet expansion can be divided into three regions: the main flow region, the compression region, and the backflow vortex region. In the main flow region the temperature and velocity of the plasma jet are relatively high and both decrease along the axial and radial direction. The pressure near the Taylor cavity head is high. The high pressure region grows gradually while the pressure value decreases. The calculated axial expansion displacement of the Taylor cavity coincides well with the measured one from experiment.

The residual stress distribution in plasma-sprayed zirconia thermal barrier coatings subjected to cyclic thermal gradient testing was evaluated using Raman piezospectroscopy and finite element computation. The thermal gradient testing (approximately 440 ° C / mm at temperature), consisted of repeated front-side heating with a flame and constant cooling of the back-side of the substrate either with front-side radiative cooling only or with additional forced air cooling between the heating cycles. The coatings exhibited characteristic “mud-cracking” with the average crack spacing dependent on the cooling treatment. This is consistent with finite element calculations and Raman spectroscopy measurements in which the sudden drop in coating surface temperature on initial cooling leads to a large biaxial tension at the surface. The key to proper interpretation of the Raman shifts is that the stress-free Raman peaks need to be corrected for shifts associated with the evolution of the metastable tetragonal phase with aging.

Ceramic materials applied by air plasma spray are used as components of thermal barrier coatings. As it has been found that such coatings also dissipate significant amounts of energy during vibration, they can also contribute to reducing the amplitude of resonant vibrations. In order to select a coating material for this purpose, or to adjust application parameters for increased dissipation, it is important that the specific mechanism, by which such dissipation occurs, be known and understood. It has been suggested that the dissipative mechanism in air plasma sprayed coatings is friction, along interfaces arising from defects between and within the “splats” created during application. An analysis, similar to that for the dissipation in a lap joint, is developed for an idealized microstructure characteristic of such coatings. A measure of damping (loss modulus) is extracted, and the amplitude dependence is found to be similar to that observed with actual coating materials. A critical combination of parameters is identified, and variations within the microstructure are accounted for by representing values through a distribution. The effective or average value of the storage (Young’s) modulus is also developed, and expressed in terms of the parameters of the microstructure. The model appears to provide a satisfactory analytical representation of the damping and stiffness of these materials.

During reentry from space, a layer of high temperature air ( > 3000 K ) is formed extending tens of centimeters from the surface of the vehicle, well out into the high speed flow regime. Magnetohydrodynamics (MHD) can then be used to generate power by projecting magnetic fields outside the vehicle into the conducting air stream and collecting the resulting current. Here, we analyze a multifunctional MHD panel which generates the requisite magnetic fields, protects the vehicle from high temperatures, and is structurally stiff and strong. The analysis shows that a magnetic system weighing approximately 110 kg can generate 0.6 MW of power for 1000 s .

To understand the abnormal flow conditions caused by the boundary irregularities in diseased vessels, an analytical solution is obtained for the steady laminar flow of an incompressible Newtonian fluid in a channel with irregular surfaces where the spread of the surface roughness is large compared to the mean width of the channel. The hydrodynamic solution is then used to obtain the effects of wall roughness upon the blood oxygenation in a membrane oxygenator. The effects of various pertinent parameters upon the flow field, energy loss, and oxygen concentration, and possible occurrence of separation and reattachment are examined for symmetric and nonsymmetric channels with sinusoidal variation. It is found that when the blood is assumed to behave like a homogeneous fluid the wall irregularity has a strong effect on local oxygen concentration distribution, but has little effect on the saturation length. The saturation length is found to be of the order of 3/2 (1 + FS 0 /P 0 )R e S c d for a channel with, or without, wall irregularity. Therefore, the secondary flows induced by the cell-plasma and cell-cell interaction is more likely the primary mechanism for a vast increase in oxygenation efficiency using wavy channels reported by Kolobow, et al.

A theoretical and experimental study was made of the hydrodynamic drag on a small sphere moving relative to a plasma in local thermodynamic equilibrium. The results have application to velocity measurement in ionized gases using the technique of injecting small particles and following their motion as a function of time. The previously available sphere drag results for fluids with properties which vary linearly with temperature are shown to be in error by as much as 40 percent for an argon plasma at 13,000 deg K, for example, because large temperature gradients occur in the vicinity of the sphere where fluid properties vary nonlinearly with temperature. A new drag calculation for a sphere Reynolds number of zero has been made for an argon plasma taking into account nonlinear variations of transport properties with temperature. Sphere deflection measurements in an argon plasma have been made at Reynolds numbers between 0.3 and 1.5. The interpretation of these measurements in terms of sphere drag is subject to confirmation of the plasma transport properties used in the data reduction, but the difference between the measured drag and the drag calculated for zero Reynolds number appears to be approximately the same as in the classical case for invariant fluid properties.

A formulation of the finite-element method for both two-dimensional and axisymmetric slow viscous flow is presented. Its application to flow of large particles in a channel or a circular cylindrical tube is discussed. The particles are assumed to be disk-shaped and are disposed axisymmetrically in the tube. The velocity profiles, the pressure gradient, and the shear stress on the wall are determined as functions of kinematic parameters. The conditions are selected to represent an idealization of the motion of red blood cells and plasma in capillary blood vessels.

The drag of an adiabatic flat plate in an ionized gas for a constant magnetic field applied to the boundary layer on the plate is found by a momentum integral approximation of von Karman. Laminar, two-dimensional flow, zero pressure gradient, small magnetic Reynolds number, and negligible electrical conductivity outside the boundary layer are assumed. The solution is valid in particular to a continuous, perfect-gas plasma, of unitary Prandtl number, and for conditions when the interaction parameter is very small. The solution shows the following effects: The adiabatic wall temperature is independent of the magnetic field; there is an increase in the boundary-layer thickness as the magnetic-field strength is increased; and the viscous drag coefficient decreases whereas the coefficient of total drag increases.