We study nondiffracting accelerating paraxial optical beams in periodic potentials, in both the linear and the nonlinear domains. In particular, we show that only a unique class of z-dependent lattices can support a true accelerating diffractionless beam. Accelerating lattice solitons, autofocusing beams and accelerating bullets in optical lattices are systematically examined.

In 1798 J.-L. Lagrange published an extensive book on the solution of numerical equations. Lagrange had developed a general systematic algorithm for detecting, isolating, and approximating all real and complex roots of a polynomial equation with real coeecients, with arbitrary precision. In contrast to Newton's Method, Lagrange's algorithm is guaranteed to converge. We discuss some lesser known...

Li-ion batteries are the essential energy-storage building blocks of modern society. However, producing ultra-high electrochemical performance in safe and sustainable for example, e-mobility, portable stationary applications, demands overcoming major technological challenges. Materials engineering new chemistries key aspects to achieving this objective, intimately linked use advanced characteri...

Local algorithms for obtaining pivot orderings for sparse symmetric coefficient matrices are reviewed together with their mathematical background, appropriate data structures and details of efficient implementation. Heuristics that go beyond the classical Minimum Degree and Minimum Local Fill scoring functions are discussed, illustrated, improved and extensively tested on a test suite of matric...

High-dose therapy with autologous hematopoietic progenitor cell support is effective treatment for patients with a variety of high-risk malignancies. Accelerating of marrow recovery from near-lethal or lethal toxicity with hematopoietic cell support improves the safety and cost effectiveness of the high-dose regimens. Peripheral blood progenitor cells will soon replace marrow as the major sourc...

Many speed-up techniques developed for accelerating the computation of shortest paths in road networks, like reach or contraction hierarchies, are based on the property that some streets are ’more important’ than others, e.g. on long routes the usage of an interstate is almost inevitable. In grids there is no obvious hierarchy among the edges, especially if the costs are uniform. Nevertheless w...

This whitepaper describes the programming techniques used to develop an auto-tuning compression scheme for sparse matrices with respect to accelerating matrix-vector multiplication and minimizing its energy footprint, as well as a method for extracting a power profile from a corresponding implementation of the conjugate gradient method. Using two example systems, we show how these techniques ca...