Asteroid identification using statistical orbital inversion methods

An efficient and statistically robust solution for the identification of asteroids among numerous sets of astrometry is presented. In particular, numerical methods have been developed for the short-term identification of asteroids at discovery, and for the long-term identification of scarcely observed asteroids over apparitions, a task which has been lacking a robust method until now. The methods are based on the solid foundation of statistical orbital inversion properly taking into account the observational uncertainties, which allows for the detection of practically all correct identifications. Through the use of dimensionality-reduction techniques and efficient data structures, the exact methods have a loglinear, that is, O(nlog(n)), computational complexity, where n is the number of included observation sets. The methods developed are thus suitable for future large-scale surveys which anticipate a substantial increase in the astrometric data rate. Due to the discontinuous nature of asteroid astrometry, separate sets of astrometry must be linked to a common asteroid from the very first discovery detections onwards. The reason for the discontinuity in the observed positions is the rotation of the observer with the Earth as well as the motion of the asteroid and the observer about the Sun. Therefore, the aim of identification is to find a set of orbital elements that reproduce the observed positions with residuals similar to the inevitable observational uncertainty. Unless the astrometric observation sets are linked, the corresponding asteroid is eventually lost as the uncertainty of the predicted positions grows too large to allow successful follow-up. Whereas the presented identification theory and the numerical comparison algorithm are generally applicable, that is, also in fields other than astronomy (e.g., in the identification of space debris), the numerical methods developed for asteroid identification can immediately be applied to all objects on heliocentric orbits with negligible effects due to non-gravitational forces in the time frame of the analysis. The methods developed have been successfully applied to various identification problems. Simulations have shown that the methods developed are able to find virtually all correct linkages despite challenges such as numerous scarce observation sets, astrometric uncertainty, numerous objects confined to a limited region on the celestial sphere, long linking intervals, and substantial parallaxes. Tens of previously unknown main-belt asteroids have been identified with the short-term method in a preliminary study to locate asteroids among numerous unidentified sets of single-night astrometry of moving objects, and scarce astrometry obtained nearly simultaneously with Earth-based and space-based telescopes has been successfully linked despite a substantial parallax. Using the long-term method, thousands of realistic 3-linkages typically spanning several apparitions have so far been found among designated observation sets each spanning less than 48 hours.

Stability of an unsupported vertical circular excavation in clays under undrained condition

By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (gamma H/c(o)) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; gamma = unit weight, H., height of the excavation and c(o) = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature.(C) 2009 Elsevier Ltd. All rights reserved.

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t* >= 5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state. (C) 2010 Elsevier Ltd. All rights reserved.

Lightcurve inversion for asteroid spins and shapes

Knowledge of the physical properties of asteroids is crucial in many branches of solar-system research. Knowledge of the spin states and shapes is needed, e.g., for accurate orbit determination and to study the history and evolution of the asteroids. In my thesis, I present new methods for using photometric lightcurves of asteroids in the determination of their spin states and shapes. The convex inversion method makes use of a general polyhedron shape model and provides us at best with an unambiguous spin solution and a convex shape solution that reproduces the main features of the original shape. Deriving information about the non-convex shape features is, in principle, also possible, but usually requires a priori information about the object. Alternatively, a distribution of non-convex solutions, describing the scale of the non-convexities, is also possible to be obtained. Due to insufficient number of absolute observations and inaccurately defined asteroid phase curves, the $c/b$-ratio, i.e., the flatness of the shape model is often somewhat ill-defined. However, especially in the case of elongated objects, the flatness seems to be quite well constrained, even in the case when only relative lightcurves are available. The results prove that it is, contrary to the earlier misbelief, possible to derive shape information from the lightcurve data if a sufficiently wide range of observing geometries is covered by the observations. Along with the more accurate shape models, also the rotational states, i.e., spin vectors and rotation periods, are defined with improved accuracy. The shape solutions obtained so far reveal a population of irregular objects whose most descriptive shape characteristics, however, can be expressed with only a few parameters. Preliminary statistical analyses for the shapes suggests that there are correlations between shape and other physical properties, such as the size, rotation period and taxonomic type of the asteroids. More shape data of, especially, the smallest and largest asteroids, as well as the fast and slow rotators is called for in order to be able to study the statistics more thoroughly.

Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (eta, tau). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.

Free convection heat transfer from vertical cylinders and wires

Free convection heat transfer from vertical long cylinders and wires were investigated experimentally. The experiments were designed to check the analytical results and the radius of curvature criteria formulated by the same authors. The results for water, the fluid medium used in the present set of experiments, are in excellent agreement with the theory. The results of Hama, Recesso and Christiaens, Kyte, Madden and Piret, in air are also shown to be in close agreement with proposed correlations.

Free convection heat transfer in vertical annuli

Free convection heat transfer in vertical concentric, cylindrical annuli is investigated analytically and experimentally. The approximate double boundary layer model used by Emery and Chu for the case of vertical parallel plates is extended to the present case in obtaining heat transfer correlations in laminar free convection. Different correlations for the inner cylinder depending on the radius to the length ratio of the inner cylinder and the Rayleigh number, were used in the derivation of correlations for the annuli. The results for the case of short cylinders inside tubes are in agreement (within about 10 per cent) with the existing correlations. For other cases, namely long cylinders in annuli and wires in annuli, experiments conducted show the agreement of the analysis with experiments.

Free convection heat transfer between vertical parallel plates

A new mathematical model for the solution of the problem of free convection heat transfer between vertical parallel flat isothermal plates under isothermal boundary conditions, has been presented. The set of boundary layer equations used in the model are transformed to nonlinear coupled differential equations by similarity type variables as obtained by Ostrach for vertical flat plates in an infinite fluid medium. By utilising a parameter ηw* to represent the outer boundary, the governing differential equations are solved numerically for parametric values of Pr = 0.733. 2 and 3, and ηw* = 0.1, 0.5, 1, 2, 3, 4, ... and 8.0. The velocity and temperature profiles are presented. Results indicate that ηw* can effectively classify the system into (1) thin layers where conduction predominates, (2) intermediate layers and (3) thick layers whose results can be predicted by the solutions for vertical flat plates in infinite fluid medium. Heat transfer correlations are presented for the 3 categories. Several experimental and analytical results available in the literature agree with the present correlations.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Free convection heat transfer from vertical cylinders part II: Exponential surface temperature variation

Investigation on laminar free convection heat transfer from vertical cylinders and wires having a surface temperature variation of the form TW - T∞ = M emx are presented. As in Part I for power law surface temperature variation, the axisymmetric boundary layer equations of mass, momentum and energy are transformed to more convenient forms and solved numerically. The second approximation refines the results of the first upto a maximum of only 2%. Analysis of the results indicates that cylinders can be classified into the same three categories as in Part I, namely, short cylinders, long cylinders, and wires, heat transfer and fluid flow correlations being developed for each case.

Unsteady mixed convection flow of a thermomicropolar fluid on a long thin vertical cylinder

The unsteady laminar mixed convection boundary layer flow of a thermomicropolar fluid over a long thin vertical cylinder has been studied when the free stream velocity varies with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite difference scheme in combination with the quasilinearization technique. The results show that the buoyancy, curvature and suction parameters, in general, enhance the skin friction, heat transfer and gradient of microrotation, but the effect of injection is just opposite. The skin friction and heat transfer for the micropolar fluid are considerably less than those for the Newtonian fluids. The effect of microrotation parameter is appreciable only on the microrotation gradient. The effect of the Prandtl number is appreciable on the skin friction, heat transfer and gradient of microtation.

Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optinial dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator).

A neuro-adaptive augmented optimal dynamic inversion approach for effective and efficient treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.

Vertical profile of aerosol single scattering albedo over west coast of India during W_ICARB

Altitude profile of aerosol Single Scattering Albedo (SSA), derived from simultaneous in-situ airborne measurements of the coefficients of aerosol absorption and scattering off the west coast of India over the Arabian Sea (AS), during January 2009 is presented. While both the absorption and scattering coefficients decreased with altitude, their vertical structure differed significantly. Consequently, the derived SSA, with a surface value of 0.94, decreased with altitude, illustrating increasing relative dominance of aerosol absorption at higher altitudes. Altitude profile of SSA, when examined in conjunction with that of hemispheric backscatter fraction, revealed that the continental influence on the aerosol properties was higher at higher altitude, rather than the effect of marine environment. During an east-west transect across the peninsular India at an altitude of similar to 2500 m (free troposphere), it was found that the aerosol scattering coefficients remained nearly the same over both east and west coasts. (C) 2010 Elsevier Ltd. All rights reserved.