Relative Motion Parameters Research Articles

A modification of the non-Markovian encounter theory. III. Hopping and diffusion mechanisms of reactions

Abstract The exact kinetic law has been calculated for the hopping mechanism of the reaction A + B → B with allowance for the mobility of both reactants. The binary kinetics depending solely on the relative motion parameters has been extracted. It is shown that in the same time interval the binary kinetics is correctly described by both the non-Markovian differential theory and the encounter theory. The binary kinetics extraction principle is formulated. Generalization of this principle to diffusion motion shows that the encounter theory does not allow for all necessary binary terms, and, therefore, needs modification. The required modification of the kernel of the encounter theory equation for the reactions A + B → B and A + B → C has been performed.

Time-to-go estimation from infrared images

This application paper deals with the problem of an aircraft flying towards a rendezvous point using passive image data to calculate the flight duration. A technique is described which estimates time-to-go from a sequence of infrared images by applying a generalisation of a conventional correlation process. The method relies on measurements from a multiple point correlation tracker, which is able to track a landmark or object. It is shown that a difference squared correlator is equivalent to the measurement equation of a parameter estimation scheme with tracking offsets as states. The offsets are measured to subpixel precision and the measurement errors are related to the curvature of the correlation surface. Correlator errors are shown to exhibit a spatiotemporal correlation structure. A simple relative motion model is postulated, which uses magnification, rotation and translation, with the instantaneous measure of time-to-go related to the magnification scale factor. Estimates of the relative motion parameters are derived by solving a set of linear equations. The mapping of tracking errors to errors in the estimated motion parameters is investigated. A series of experiments using simulated data is detailed and the results are discussed. In the latter stages of flight, the time-to-go estimates are shown to give acceptable results for many applications.

Testing models of the Tertiary paleomagnetic field

We examine selected paleomagnetic data of Tertiary age in order to assess previously suggested models of the non-dipole portion of the paleomagnetic field. Data from three localities on the African plate (from DSDP Leg 73, ODP Leg 115 and from Gubbio) indicate that the axial octupole contribution was near zero in the Paleocene and was likely no greater than 5–6% of the axial dipole in the Oligocene. Additional data from North America, which can be linked to Africa using well-known relative plate motion parameters, suggest that a positive axial quadrupole field has been present throughout the Tertiary. To investigate some of the practical consequences of these estimates, we apply a non-dipole field model (3 to 4% g 2 0/g 1 0, 0% g 3 0/g 1 0) to paleomagnetic data from two ODP sites on the African plate (Sites 710, 711) and from the Deccan Traps. We show that paleomagnetic directions from these deep-sea sediments and from this flood basalt province appear consistent with a fixed hotspot model, suggesting in particular that there has been little or no Cenozoic drift of the Réunion hotspot.

New autofocusing technique for SAR images based on the Wigner-Ville distribution

High resolution images can be obtained with synthetic aperture radars, by exploiting the motion between the aircraft carrying the radar and the observed scene, if the relative motion parameters are known exactly. There exist some techniques for estimating these parameters from the collected data, but only for specific cases (linear and quadratic phase error). A technique for compensating phase errors whatever their time variation is proposed. The proposed technique is based on a joint time-frequency analysis of the received signal, carried out using the Wigner-Ville distribution.

Simplification of the Matrix method of linkage analysis by division of a mechanism into unclosed kinematic chains

This paper suggests a method of analysis of spatial linkages based on using matrices of order 4 and imaginary unclosure of the mechanism contour into open kinematic chains. Employment of this method allows: (a) development of the matrix equation of contour closure, (b) simplification of the relative orientation of the coordinate systems used, and (c) division of the system of equations which connect the parameters of relative motion on subsystems that simplify the analysis of the mechanism. The method offered here has been used in an investigation of the precision of motion transference by Oldham's coupling when the axes are skewed.