Guidance, flight mechanics and trajectory optimization. Volume 12 - Relative motion, guidance equations for terminal rendezvous

Equations of relative motion and guidance for orbital transfer and docking maneuvers in spacecraft rendezvou

On the generation of internal waves by tidal flow over a sill----a possible nonlinear mechanism

The generation of internal waves in a two layer tidal channel containing a sill is considered. The distorted free surface associated with the locally accelerated tidal flow in the vicinity of the sill is assumed to be the driving force for internal waves. A simplified, nonrigorous model, which incorporates this forcing mechanism, is developed and predicts that internal waves should be generated at twice the tidal frequency as well as at the tidal frequency...

Minimizing Communication in Linear Algebra

In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In 2004 Irony, Toledo and Tiskin gave a new proof of this result and extended it to the parallel case. In both cases the lower bound may be expressed as $\Omega$(#arithmetic operations / $\sqrt{M}$), where M is the size of the fast memory (or local memory in the parallel case). Here we generalize these results to a much wider variety of algorithms, including LU factorization, Cholesky factorization, $LDL^T$ factorization, QR factorization, algorithms for eigenvalues and singular values, i.e., essentially all direct methods of linear algebra. The proof works for dense or sparse matrices, and for sequential or parallel algorithms. In addition to lower bounds on the amount of data moved (bandwidth) we get lower bounds on the number of messages required to move it (latency). We illustrate how to extend our lower bound technique to compositions of linear algebra operations (like computing powers of a matrix), to decide whether it is enough to call a sequence of simpler optimal algorithms (like matrix multiplication) to minimize communication, or if we can do better. We give examples of both. We also show how to extend our lower bounds to certain graph theoretic problems. We point out recently designed algorithms for dense LU, Cholesky, QR, eigenvalue and the SVD problems that attain these lower bounds; implementations of LU and QR show large speedups over conventional linear algebra algorithms in standard libraries like LAPACK and ScaLAPACK. Many open problems remain.Comment: 27 pages, 2 table

Guidance, flight mechanics and trajectory optimization. Volume 11 - Guidance equations for orbital operations

Mathematical formulation of guidance equations and solutions for orbital space mission

Physical Electronics

Contains research objectives and reports on one research project

Guidance, flight mechanics and trajectory optimization. Volume 6 - The N-body problem and special perturbation techniques

Analytical formulations and numerical integration methods for many body problem and special perturbative technique

Guidance, Flight Mechanics and Trajectory Optimization. Volume 15 - Application of Optimization Techniques

Pontryagin maximum principle, calculus of variations, and dynamic programming optimization techniques applied to trajectory and guidance problem

Element orbitals for Kohn-Sham density functional theory

We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, which is a small part of the global domain containing multiple atoms. We demonstrate that the resulting basis set achieves meV accuracy for 3D densely packed systems with a small number of basis functions per atom. The procedure is applicable to insulating and metallic systems

Monitoring of offshore geological carbon storage integrity: Implications of natural variability in the marine system and the assessment of anomaly detection criteria

The design of efficient monitoring programmes required for the assurance of offshore geological storage requires an understanding of the variability and heterogeneity of marine carbonate chemistry. In the absence of sufficient observational data and for extrapolation both spatially and seasonally, models have a significant role to play. In this study a previously evaluated hydrodynamic-biogeochemical model is used to characterise carbonate chemistry, in particular pH heterogeneity in the vicinity of the sea floor. Using three contrasting regions, the seasonal and short term variability are analysed and criteria that could be considered as indicators of anomalous carbonate chemistry identified. These criteria are then tested by imposing a number of randomised DIC perturbations on the model data, representing a comprehensive range of leakage scenarios. In conclusion optimal criteria and general rules for developing monitoring strategies are identified. Detection criteria will be site specific and vary seasonally and monitoring may be more efficient at periods of low dynamics. Analysis suggests that by using high frequency, sub-hourly monitoring anomalies as small as 0.01 of a pH unit or less may be successfully discriminated from natural variability – thereby allowing detection of small leaks or at distance from a leakage source. Conversely assurance of no leakage would be profound. Detection at deeper sites is likely to be more efficient than at shallow sites where the near bed system is closely coupled to surface processes. Although this study is based on North Sea target sites for geological storage, the model and the general conclusions are relevant to the majority of offshore storage sites lying on the continental shelf

A Review of Scanning Tunneling Microscope and Atomic Force Microscope Imaging of Large Biological Structures: Problems and Prospects

The application of the scanning tunneling microscope (STM) and the atomic force microscope (AFM) to the study of small biological molecules, such as DNA and smaller molecules, has received considerable attention in the literature. This paper reviews STM and AFM studies of larger biological structures such as bacterial membranes, bacteriophages, viruses, antibodies, etc. The problems encountered in these applications are emphasized, with particular reference to the unknown conduction mechanism, tip-sample interaction forces, and tip-sample convolution artifacts in the images. The latter problem is illustrated by new results from IgG antibody complexes attached to a bacterial sheath layer. A new conduction mechanism involving a graphite film overlayer is suggested. The future prospects are discussed, with emphasis on the unique capabilities of these microscopes compared to conventional electron microscopes